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(and) Tj
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(Time) Tj
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1 0 0 1 450 475 Tm
117 Tz
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(for) Tj
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(solving) Tj
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(sys) Tj
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(tems) Tj
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(of) Tj
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(in) Tj
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1 0 0 1 188 463 Tm
(one) Tj
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(spatial) Tj
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1 0 0 1 242 463 Tm
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(variable) Tj
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(and) Tj
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(time.) Tj
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(A) Tj
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(subsequent) Tj
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(paper) Tj
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(which) Tj
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(hopefully) Tj
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(benefit) Tj
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(user) Tj
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(based) Tj
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(on) Tj
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(conditions) Tj
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(time) Tj
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(be) Tj
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(making) Tj
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(known) Tj
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(function) Tj
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(of) Tj
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(time.) Tj
100 Tz
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(Section) Tj
100 Tz
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1 0 0 1 174 349 Tm
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(describes) Tj
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(the) Tj
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(class) Tj
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(of) Tj
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(PDE) Tj
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(problems) Tj
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(treated.) Tj
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(Section) Tj
100 Tz
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(3) Tj
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(discusses) Tj
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(numerical) Tj
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(method) Tj
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(the) Tj
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(method) Tj
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(space,) Tj
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(variable) Tj
100 Tz
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(order,) Tj
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100 Tz
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(time-step) Tj
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(backward) Tj
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(difference) Tj
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(procedure) Tj
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(in) Tj
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(time) Tj
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(4) Tj
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1 0 0 1 113 313 Tm
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(discusses) Tj
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(several) Tj
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(simple) Tj
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1 0 0 1 228 313 Tm
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(applications) Tj
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(5) Tj
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(mechanism) Tj
100 Tz
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(for) Tj
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(non-local) Tj
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(statements) Tj
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(be) Tj
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(made) Tj
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(about) Tj
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(solution,) Tj
100 Tz
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100 Tz
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(ODE\202s) Tj
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(in) Tj
100 Tz
1 0 0 1 164 290 Tm
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(time.) Tj
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(Section) Tj
100 Tz
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(discusses) Tj
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(used) Tj
100 Tz
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(solve) Tj
100 Tz
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(PDE) Tj
100 Tz
(-) Tj
1 0 0 1 102 278 Tm
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(ODE) Tj
100 Tz
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98 Tz
(combinations) Tj
100 Tz
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93 Tz
(and) Tj
100 Tz
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(handle) Tj
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(periodic) Tj
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(boundary) Tj
100 Tz
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96 Tz
(conditions.) Tj
100 Tz
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(7) Tj
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100 Tz
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(list) Tj
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(error) Tj
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(states) Tj
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(problems) Tj
100 Tz
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(which) Tj
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(arise) Tj
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(when) Tj
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(what) Tj
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(algorithm) Tj
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(by) Tj
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(detail.) Tj
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(I) Tj
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(gives) Tj
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(on) Tj
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100 Tz
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(gives) Tj
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(brief) Tj
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(tutorial) Tj
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1 0 0 1 202 226 Tm
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(on) Tj
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(extrapolation.) Tj
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1 0 0 1 288 226 Tm
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(Appendix) Tj
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(3) Tj
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(they) Tj
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(produce) Tj
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(an) Tj
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(approximate) Tj
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1 0 0 1 265 497 Tm
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(solution) Tj
100 Tz
1 0 0 1 304 497 Tm
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(which) Tj
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(equations) Tj
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(time-steps) Tj
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(results) Tj
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(result) Tj
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100 Tz
1 0 0 1 125 450 Tm
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(process) Tj
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(of) Tj
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1 0 0 1 214 450 Tm
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100 Tz
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100 Tz
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1 0 0 1 344 450 Tm
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(sequence) Tj
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(of) Tj
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(processes) Tj
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100 Tz
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1 0 0 1 137 423 Tm
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(step-size) Tj
100 Tz
1 0 0 1 178 423 Tm
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(order) Tj
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(mQnitor) Tj
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(is) Tj
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(available) Tj
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(carrying) Tj
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(out) Tj
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(this) Tj
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(extrapolation) Tj
100 Tz
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112 Tz
(pro) Tj
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(cess) Tj
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83 Tz
(automaticaIO~\202) Tj
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(deciding) Tj
100 Tz
1 0 0 1 241 410 Tm
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1 0 0 1 265 410 Tm
(time-step) Tj
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(8) Tj
100 Tz
1 0 0 1 319 410 Tm
(and) Tj
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96 Tz
(order) Tj
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1 0 0 1 367 410 Tm
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(should) Tj
100 Tz
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(be) Tj
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100 Tz
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100 Tz
1 0 0 1 514 410 Tm
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(the) Tj
100 Tz
1 0 0 1 100 398 Tm
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(accuracy) Tj
100 Tz
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(desired) Tj
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100 Tz
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(solution) Tj
100 Tz
1 0 0 1 100 386 Tm
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98 Tz
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100 Tz
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(time) Tj
100 Tz
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98 Tz
(integration) Tj
100 Tz
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100 Tz
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100 Tz
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100 Tz
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(no) Tj
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(need) Tj
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(for) Tj
100 Tz
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100 Tz
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100 Tz
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(worry) Tj
100 Tz
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(about) Tj
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100 Tz
1 0 0 1 277 374 Tm
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100 Tz
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(whether) Tj
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100 Tz
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(solution) Tj
100 Tz
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100 Tz
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100 Tz
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(enough.) Tj
100 Tz
1 0 0 1 125 359 Tm
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100 Tz
1 0 0 1 145 359 Tm
98 Tz
(algorithm) Tj
100 Tz
1 0 0 1 191 359 Tm
(for) Tj
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(solving) Tj
100 Tz
1 0 0 1 242 359 Tm
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(such) Tj
100 Tz
1 0 0 1 265 359 Tm
96 Tz
(PDE\202s) Tj
100 Tz
1 0 0 1 297 359 Tm
(then) Tj
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(consists) Tj
100 Tz
1 0 0 1 358 359 Tm
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100 Tz
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100 Tz
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100 Tz
1 0 0 1 172 343 Tm
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(the) Tj
100 Tz
1 0 0 1 189 343 Tm
98 Tz
(equations) Tj
100 Tz
1 0 0 1 235 343 Tm
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100 Tz
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92 Tz
(space) Tj
100 Tz
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100 Tz
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100 Tz
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100 Tz
1 0 0 1 125 328 Tm
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(Produce) Tj
100 Tz
1 0 0 1 164 328 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 172 328 Tm
(one-step) Tj
1 0 0 1 213 328 Tm
97 Tz
(method) Tj
100 Tz
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(for) Tj
1 0 0 1 266 328 Tm
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(solving) Tj
100 Tz
1 0 0 1 301 328 Tm
92 Tz
(the) Tj
100 Tz
1 0 0 1 318 328 Tm
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(resulting) Tj
100 Tz
1 0 0 1 359 328 Tm
94 Tz
(ODE\202s.) Tj
100 Tz
1 0 0 1 101 313 Tm
78 Tz
(3\)) Tj
100 Tz
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100 Tz
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(that) Tj
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(one-step) Tj
100 Tz
1 0 0 1 211 313 Tm
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100 Tz
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100 Tz
1 0 0 1 259 313 Tm
92 Tz
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100 Tz
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97 Tz
(extrapolation) Tj
100 Tz
1 0 0 1 337 313 Tm
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(step-size) Tj
100 Tz
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(order) Tj
100 Tz
1 0 0 1 424 313 Tm
97 Tz
(monitor.) Tj
100 Tz
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(4.) Tj
100 Tz
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100 Tz
1 0 0 1 158 289 Tm
86 Tz
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100 Tz
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100 Tz
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100 Tz
1 0 0 1 235 289 Tm
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(Problem.) Tj
100 Tz
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1 0 0 1 125 273 Tm
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(The) Tj
100 Tz
1 0 0 1 146 273 Tm
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(algorithm) Tj
100 Tz
1 0 0 1 192 273 Tm
97 Tz
(outlined) Tj
100 Tz
1 0 0 1 233 273 Tm
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100 Tz
1 0 0 1 245 273 Tm
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(section) Tj
100 Tz
1 0 0 1 280 273 Tm
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100 Tz
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100 Tz
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(in) Tj
100 Tz
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(detail) Tj
100 Tz
1 0 0 1 395 273 Tm
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(in) Tj
100 Tz
1 0 0 1 408 273 Tm
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(sections) Tj
100 Tz
1 0 0 1 446 273 Tm
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(8) Tj
100 Tz
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(9,) Tj
100 Tz
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(has) Tj
100 Tz
1 0 0 1 507 273 Tm
95 Tz
(been) Tj
100 Tz
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98 Tz
(implemented) Tj
100 Tz
1 0 0 1 162 261 Tm
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(in) Tj
100 Tz
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(EFL) Tj
100 Tz
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(Ratfor-\[321-like) Tj
100 Tz
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(FORTRAN) Tj
100 Tz
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96 Tz
(preprocessor) Tj
100 Tz
1 0 0 1 419 261 Tm
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(language) Tj
100 Tz
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100 Tz
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(elegance) Tj
100 Tz
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100 Tz
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(power.) Tj
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100 Tz
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(user\202s) Tj
100 Tz
1 0 0 1 325 249 Tm
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(manual) Tj
100 Tz
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100 Tz
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92 Tz
(package) Tj
100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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(differential) Tj
100 Tz
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(equations) Tj
100 Tz
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(Space) Tj
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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(preprocessor,) Tj
100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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(or) Tj
100 Tz
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(other) Tj
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100 Tz
1 0 0 1 154 213 Tm
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(preprocessing) Tj
100 Tz
1 0 0 1 218 213 Tm
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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100 Tz
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(that) Tj
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(the) Tj
100 Tz
1 0 0 1 260 198 Tm
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(current,) Tj
100 Tz
1 0 0 1 302 198 Tm
96 Tz
(preliminary) Tj
100 Tz
1 0 0 1 358 198 Tm
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(implementation) Tj
100 Tz
1 0 0 1 432 198 Tm
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(is) Tj
100 Tz
1 0 0 1 444 198 Tm
88 Tz
(still) Tj
100 Tz
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100 Tz
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100 Tz
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100 Tz
1 0 0 1 148 186 Tm
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96 Tz
(user\202s) Tj
100 Tz
1 0 0 1 220 186 Tm
96 Tz
(complaints,) Tj
100 Tz
1 0 0 1 276 186 Tm
(comments) Tj
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1 0 0 1 349 186 Tm
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(suggestions) Tj
100 Tz
1 0 0 1 405 186 Tm
92 Tz
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1 0 0 1 423 186 Tm
98 Tz
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100 Tz
1 0 0 1 480 186 Tm
93 Tz
(before) Tj
100 Tz
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(time.) Tj
100 Tz
1 0 0 1 106 630 Tm
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(output) Tj
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1 0 0 1 159 630 Tm
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(from) Tj
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(altered) Tj
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(altered) Tj
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(altered) Tj
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1 0 0 1 163 549 Tm
98 Tz
(Precision) Tj
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1 0 0 1 207 549 Tm
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(version) Tj
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1 0 0 1 242 549 Tm
(of) Tj
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(calling) Tj
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1 0 0 1 412 549 Tm
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(sequence) Tj
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(cisely) Tj
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(the) Tj
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(same) Tj
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(as) Tj
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106 Tz
(that) Tj
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(Posts,) Tj
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97 Tz
(floating-point) Tj
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1 0 0 1 371 537 Tm
(arguments) Tj
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(Double) Tj
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1 0 0 1 460 537 Tm
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(Precision,) Tj
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1 0 0 1 139 525 Tm
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91 Tz
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(amount) Tj
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92 Tz
(space) Tj
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(library) Tj
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1 0 0 1 233 513 Tm
105 Tz
(neglecting) Tj
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(lower) Tj
1 0 0 1 308 513 Tm
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(order) Tj
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1 0 0 1 335 513 Tm
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(terms,) Tj
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1 0 0 1 106 477 Tm
97 Tz
(Double) Tj
100 Tz
1 0 0 1 142 477 Tm
98 Tz
(Precision) Tj
100 Tz
1 0 0 1 185 477 Tm
96 Tz
(words) Tj
100 Tz
1 0 0 1 215 477 Tm
94 Tz
(\(storage) Tj
100 Tz
1 0 0 1 254 477 Tm
(units\).) Tj
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94 Tz
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98 Tz
(examples) Tj
100 Tz
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96 Tz
(given) Tj
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93 Tz
(below,) Tj
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(and) Tj
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(intended) Tj
1 0 0 1 406 461 Tm
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(both) Tj
100 Tz
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97 Tz
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93 Tz
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98 Tz
(prototypes) Tj
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(for) Tj
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(a) Tj
100 Tz
1 0 0 1 265 449 Tm
96 Tz
(prospective) Tj
100 Tz
1 0 0 1 319 449 Tm
90 Tz
(user.) Tj
100 Tz
1 0 0 1 347 449 Tm
97 Tz
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100 Tz
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98 Tz
(contemplating) Tj
100 Tz
1 0 0 1 451 449 Tm
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(using) Tj
100 Tz
1 0 0 1 478 449 Tm
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(well) Tj
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97 Tz
(advised) Tj
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97 Tz
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1 0 0 1 278 436 Tm
95 Tz
(program,) Tj
100 Tz
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92 Tz
(which) Tj
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97 Tz
(invokes) Tj
100 Tz
1 0 0 1 393 436 Tm
96 Tz
(those) Tj
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94 Tz
(capabilities) Tj
100 Tz
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100 Tz
1 0 0 1 520 436 Tm
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(the) Tj
100 Tz
1 0 0 1 106 425 Tm
(intended) Tj
1 0 0 1 148 425 Tm
97 Tz
(problem) Tj
100 Tz
1 0 0 1 188 425 Tm
82 Tz
(will) Tj
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1 0 0 1 207 425 Tm
(require,) Tj
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(and) Tj
1 0 0 1 265 425 Tm
98 Tz
(keypunch) Tj
100 Tz
1 0 0 1 311 425 Tm
83 Tz
(it) Tj
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1 0 0 1 321 425 Tm
(\(or) Tj
1 0 0 1 338 425 Tm
96 Tz
(obtain) Tj
100 Tz
1 0 0 1 369 425 Tm
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(a) Tj
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1 0 0 1 376 425 Tm
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(copy) Tj
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(of) Tj
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100 Tz
1 0 0 1 471 425 Tm
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(code) Tj
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1 0 0 1 495 425 Tm
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100 Tz
1 0 0 1 520 425 Tm
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(running) Tj
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92 Tz
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98 Tz
(example,) Tj
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1 0 0 1 280 412 Tm
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1 0 0 1 300 412 Tm
96 Tz
(confirming) Tj
100 Tz
1 0 0 1 352 412 Tm
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(the) Tj
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1 0 0 1 370 412 Tm
98 Tz
(correctness) Tj
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(the) Tj
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1 0 0 1 457 412 Tm
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1 0 0 1 105 401 Tm
(and) Tj
1 0 0 1 125 401 Tm
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(BC) Tj
100 Tz
1 0 0 1 142 401 Tm
(subroutines) Tj
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93 Tz
(specifying) Tj
100 Tz
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92 Tz
(the) Tj
100 Tz
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92 Tz
(PDE-BC) Tj
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89 Tz
(may) Tj
100 Tz
1 0 0 1 327 401 Tm
93 Tz
(simply) Tj
100 Tz
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80 Tz
(be) Tj
100 Tz
1 0 0 1 373 401 Tm
(altered) Tj
1 0 0 1 407 401 Tm
88 Tz
(to) Tj
100 Tz
1 0 0 1 420 401 Tm
96 Tz
(solve) Tj
100 Tz
1 0 0 1 447 401 Tm
92 Tz
(the) Tj
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1 0 0 1 465 401 Tm
96 Tz
(user\202s) Tj
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1 0 0 1 494 401 Tm
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(problem.) Tj
100 Tz
1 0 0 1 105 389 Tm
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100 Tz
1 0 0 1 129 389 Tm
96 Tz
(progression) Tj
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1 0 0 1 183 389 Tm
96 Tz
(makes) Tj
100 Tz
1 0 0 1 215 389 Tm
83 Tz
(it) Tj
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1 0 0 1 225 389 Tm
96 Tz
(much) Tj
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1 0 0 1 253 389 Tm
(more) Tj
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88 Tz
(likely) Tj
100 Tz
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94 Tz
(that) Tj
100 Tz
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92 Tz
(the) Tj
100 Tz
1 0 0 1 346 389 Tm
94 Tz
(user) Tj
100 Tz
1 0 0 1 369 389 Tm
82 Tz
(will) Tj
100 Tz
1 0 0 1 388 389 Tm
92 Tz
(easily) Tj
100 Tz
1 0 0 1 416 389 Tm
94 Tz
(produce) Tj
100 Tz
1 0 0 1 455 389 Tm
75 Tz
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100 Tz
1 0 0 1 463 389 Tm
97 Tz
(correct) Tj
100 Tz
1 0 0 1 497 389 Tm
95 Tz
(program) Tj
100 Tz
1 0 0 1 106 377 Tm
94 Tz
(unit) Tj
100 Tz
1 0 0 1 127 377 Tm
92 Tz
(for) Tj
100 Tz
1 0 0 1 143 377 Tm
92 Tz
(the) Tj
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1 0 0 1 160 377 Tm
97 Tz
(problem) Tj
100 Tz
1 0 0 1 200 377 Tm
(at) Tj
1 0 0 1 211 377 Tm
92 Tz
(hand.) Tj
100 Tz
1 0 0 1 106 353 Tm
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1 0 0 1 150 353 Tm
75 Tz
(1.) Tj
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1 0 0 1 131 337 Tm
83 Tz
(As) Tj
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1 0 0 1 146 337 Tm
75 Tz
(a) Tj
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1 0 0 1 154 337 Tm
93 Tz
(simple) Tj
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(example) Tj
100 Tz
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(of) Tj
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92 Tz
(the) Tj
100 Tz
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93 Tz
(use) Tj
100 Tz
1 0 0 1 274 337 Tm
(of) Tj
1 0 0 1 286 337 Tm
96 Tz
(Posts,) Tj
100 Tz
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97 Tz
(consider) Tj
100 Tz
1 0 0 1 356 337 Tm
94 Tz
(solving) Tj
100 Tz
1 0 0 1 391 337 Tm
92 Tz
(the) Tj
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1 0 0 1 408 337 Tm
96 Tz
(scalar) Tj
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1 0 0 1 436 337 Tm
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(heat) Tj
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1 0 0 1 457 337 Tm
(equation) Tj
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1 0 0 1 139 319 Tm
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(Ut) Tj
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/F5 5 Tf
1 0 0 1 150 319 Tm
167 Tz
(=) Tj
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/F12 10 Tf
1 0 0 1 161 319 Tm
121 Tz
(u~+g\(t,x\)) Tj
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/F9 11 Tf
1 0 0 1 227 319 Tm
91 Tz
(on) Tj
100 Tz
1 0 0 1 246 319 Tm
95 Tz
(\(0,1\)) Tj
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1 0 0 1 512 319 Tm
90 Tz
(\(4.1\)) Tj
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1 0 0 1 106 301 Tm
104 Tz
(where) Tj
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1 0 0 1 136 301 Tm
(the) Tj
1 0 0 1 153 301 Tm
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(source) Tj
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1 0 0 1 185 301 Tm
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(term) Tj
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1 0 0 1 208 301 Tm
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(g\(t,x\)) Tj
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1 0 0 1 242 301 Tm
83 Tz
(is) Tj
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1 0 0 1 252 301 Tm
107 Tz
(chosen) Tj
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1 0 0 1 286 301 Tm
67 Tz
(\() Tj
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(g) Tj
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1 0 0 1 303 301 Tm
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110 Tz
(\(x~,) Tj
5 Ts

(2) Tj
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(\)) Tj
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1 0 0 1 370 301 Tm
(so) Tj
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(that) Tj
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(the) Tj
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106 Tz
(solution) Tj
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83 Tz
(is) Tj
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75 Tz
(a) Tj
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104 Tz
(known) Tj
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119 Tz
(func) Tj
100 Tz
(-) Tj
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(tion,) Tj
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115 Tz
(u\(t,x\)) Tj
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1 0 0 1 163 284 Tm
167 Tz
(=) Tj
100 Tz
/F8 9 Tf
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87 Tz
(ext.) Tj
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94 Tz
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(boundary) Tj
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98 Tz
(conditions) Tj
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92 Tz
(are) Tj
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(then) Tj
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(to) Tj
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1 0 0 1 389 284 Tm
90 Tz
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(=) Tj
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1 0 0 1 512 254 Tm
163 Tz
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100 Tz
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112 Tz
(u\(t,1\)) Tj
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/F5 5 Tf
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167 Tz
(=) Tj
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(with) Tj
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1 0 0 1 128 214 Tm
92 Tz
(initial) Tj
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1 0 0 1 156 214 Tm
98 Tz
(conditions) Tj
100 Tz
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1 0 0 1 139 195 Tm
111 Tz
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167 Tz
(=) Tj
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67 Tz
(I) Tj
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(.) Tj
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163 Tz
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100 Tz
/F9 11 Tf
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94 Tz
(The) Tj
100 Tz
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93 Tz
(following) Tj
100 Tz
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95 Tz
(program) Tj
100 Tz
1 0 0 1 237 174 Tm
(unit,) Tj
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97 Tz
(written) Tj
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88 Tz
(in) Tj
100 Tz
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96 Tz
(Ratfor) Tj
100 Tz
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(solves) Tj
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113 Tz
(\(4.l\)-\(4.3\)) Tj
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105 Tz
(using) Tj
100 Tz
1 0 0 1 476 174 Tm
104 Tz
(Posts,) Tj
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106 Tz
(with) Tj
100 Tz
1 0 0 1 529 174 Tm
75 Tz
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96 Tz
(cubic) Tj
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1 0 0 1 134 163 Tm
92 Tz
(B-spline) Tj
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1 0 0 1 175 163 Tm
(\(k) Tj
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1 0 0 1 188 163 Tm
171 Tz
(=) Tj
100 Tz
/F10 11 Tf
1 0 0 1 199 163 Tm
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100 Tz
1 0 0 1 254 708 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 272 708 Tm
83 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 296 708 Tm
63 Tz
(\(4.2\)) Tj
100 Tz
1 0 0 1 322 708 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 117 691 Tm
105 Tz
(Subroutine) Tj
100 Tz
1 0 0 1 190 691 Tm
89 Tz
(BC\() Tj
100 Tz
/F2 8 Tf
1 0 0 1 211 691 Tm
50 Tz
(t) Tj
100 Tz
/F1 10 Tf
1 0 0 1 218 691 Tm
103 Tz
(,L,R,U,Ux,Ut) Tj
100 Tz
1 0 0 1 296 691 Tm
92 Tz
(,Uxt) Tj
100 Tz
1 0 0 1 323 691 Tm
(,nu,V,Vt) Tj
1 0 0 1 376 691 Tm
88 Tz
(,nv,) Tj
100 Tz
1 0 0 1 209 678 Tm
106 Tz
(B,BU,BUx,BUt,BUxt) Tj
100 Tz
1 0 0 1 323 678 Tm
98 Tz
(,BV,BVt\)) Tj
100 Tz
1 0 0 1 117 655 Tm
96 Tz
(Real) Tj
100 Tz
/F2 8 Tf
1 0 0 1 152 655 Tm
25 Tz
(t) Tj
100 Tz
/F1 10 Tf
1 0 0 1 158 655 Tm
(,L,R,U\(2\)) Tj
1 0 0 1 217 655 Tm
97 Tz
(.Ux\(2\)) Tj
100 Tz
1 0 0 1 257 655 Tm
83 Tz
(,Ut) Tj
100 Tz
1 0 0 1 276 655 Tm
78 Tz
(\(2\)) Tj
100 Tz
1 0 0 1 296 655 Tm
92 Tz
(,Uxt) Tj
100 Tz
1 0 0 1 323 655 Tm
83 Tz
(\(2\)) Tj
100 Tz
1 0 0 1 342 655 Tm
83 Tz
(,V\() Tj
100 Tz
1 0 0 1 362 655 Tm
67 Tz
(I\)) Tj
100 Tz
1 0 0 1 375 655 Tm
83 Tz
(,Vt) Tj
100 Tz
1 0 0 1 395 655 Tm
78 Tz
(\(I\)) Tj
100 Tz
1 0 0 1 150 644 Tm
73 Tz
(13\(2\)) Tj
100 Tz
1 0 0 1 178 644 Tm
94 Tz
(,BU\(2\)) Tj
100 Tz
1 0 0 1 217 644 Tm
98 Tz
(,BUx\(2\)) Tj
100 Tz
1 0 0 1 263 644 Tm
92 Tz
(,BUt) Tj
100 Tz
1 0 0 1 290 644 Tm
83 Tz
(\(2\)) Tj
100 Tz
1 0 0 1 309 644 Tm
97 Tz
(,BUxt) Tj
100 Tz
1 0 0 1 342 644 Tm
78 Tz
(\(2\)) Tj
100 Tz
1 0 0 1 363 644 Tm
94 Tz
(,BV\(2\)) Tj
100 Tz
1 0 0 1 402 644 Tm
88 Tz
(,BVt) Tj
100 Tz
1 0 0 1 428 644 Tm
78 Tz
(\(2\)) Tj
100 Tz
0 g
1 g
/F1 10 Tf
1 0 0 1 117 619 Tm
73 Tz
(13\(1\)) Tj
100 Tz
1 0 0 1 162 619 Tm
108 Tz
(U\(I\)-l.OeO) Tj
100 Tz
1 0 0 1 117 607 Tm
73 Tz
(13\(2\)) Tj
100 Tz
1 0 0 1 162 607 Tm
104 Tz
(U\(2\)-Exp\(t\)) Tj
100 Tz
0 g
1 g
/F1 10 Tf
1 0 0 1 254 618 Tm
114 Tz
(#) Tj
100 Tz
1 0 0 1 269 618 Tm
83 Tz
(u\() Tj
100 Tz
/F2 8 Tf
1 0 0 1 283 618 Tm
25 Tz
(t) Tj
100 Tz
/F1 10 Tf
1 0 0 1 290 618 Tm
78 Tz
(,0\)) Tj
100 Tz
1 0 0 1 261 607 Tm
127 Tz
(#u\(t,I\)Exp\(t\).) Tj
100 Tz
0 g
1 g
/F1 10 Tf
1 0 0 1 117 583 Tm
97 Tz
(BU\(I\)) Tj
100 Tz
/F9 10 Tf
1 0 0 1 155 583 Tm
117 Tz
(=) Tj
100 Tz
/F1 10 Tf
1 0 0 1 117 571 Tm
97 Tz
(BU\(2\)) Tj
100 Tz
1 0 0 1 116 547 Tm
92 Tz
(Re) Tj
100 Tz
1 0 0 1 131 547 Tm
92 Tz
(turn) Tj
100 Tz
1 0 0 1 116 523 Tm
(End) Tj
/F10 5 Tf
1 0 0 1 400 505 Tm
172 Tz
(11) Tj
100 Tz
1 0 0 1 454 505 Tm
150 Tz
(2) Tj
100 Tz
/F9 10 Tf
1 0 0 1 103 498 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 125 498 Tm
103 Tz
(following) Tj
100 Tz
1 0 0 1 170 498 Tm
111 Tz
(output) Tj
100 Tz
1 0 0 1 204 498 Tm
109 Tz
(subroutine) Tj
100 Tz
1 0 0 1 256 498 Tm
(simply) Tj
1 0 0 1 290 498 Tm
108 Tz
(prints) Tj
100 Tz
/F11 11 Tf
1 0 0 1 320 498 Tm
106 Tz
(u\(i\202,x\),) Tj
100 Tz
/F9 10 Tf
1 0 0 1 358 498 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 375 498 Tm
(x) Tj
/F5 5 Tf
1 0 0 1 385 498 Tm
167 Tz
(=) Tj
100 Tz
/F5 15 Tf
1 0 0 1 396 498 Tm
(y,) Tj
1 0 0 1 413 498 Tm
65 Tz
(-i-.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 430 498 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 469 498 Tm
(at) Tj
1 0 0 1 482 498 Tm
(the) Tj
1 0 0 1 500 498 Tm
107 Tz
(end) Tj
100 Tz
1 0 0 1 521 498 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 103 480 Tm
(each) Tj
1 0 0 1 127 480 Tm
105 Tz
(successful) Tj
100 Tz
1 0 0 1 175 480 Tm
107 Tz
(time-step.) Tj
100 Tz
1 0 0 1 226 480 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 248 480 Tm
109 Tz
(dimension) Tj
100 Tz
1 0 0 1 298 480 Tm
110 Tz
(statement) Tj
100 Tz
1 0 0 1 345 480 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 362 480 Tm
(the) Tj
1 0 0 1 380 480 Tm
106 Tz
(various) Tj
100 Tz
1 0 0 1 416 480 Tm
109 Tz
(arguments) Tj
100 Tz
1 0 0 1 466 480 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 476 480 Tm
(for) Tj
1 0 0 1 493 480 Tm
106 Tz
(arbitrary) Tj
100 Tz
/F9 10 Tf
1 0 0 1 104 468 Tm
104 Tz
(input,) Tj
100 Tz
1 0 0 1 132 468 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 152 468 Tm
106 Tz
(thus) Tj
100 Tz
1 0 0 1 174 468 Tm
93 Tz
(will) Tj
100 Tz
1 0 0 1 193 468 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 210 468 Tm
(be) Tj
1 0 0 1 224 468 Tm
108 Tz
(repeated) Tj
100 Tz
1 0 0 1 265 468 Tm
(in) Tj
1 0 0 1 276 468 Tm
108 Tz
(subsequent) Tj
100 Tz
1 0 0 1 329 468 Tm
105 Tz
(examples.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 116 451 Tm
105 Tz
(Subroutine) Tj
100 Tz
1 0 0 1 188 451 Tm
106 Tz
(Handle\(tO,UO,VO,) Tj
100 Tz
1 0 0 1 296 451 Tm
67 Tz
(tI) Tj
100 Tz
1 0 0 1 309 451 Tm
78 Tz
(,UI) Tj
100 Tz
1 0 0 1 329 451 Tm
83 Tz
(,Vl) Tj
100 Tz
1 0 0 1 349 451 Tm
106 Tz
(,nu,nxmk,nv,k,X,nx,dt,) Tj
100 Tz
1 0 0 1 494 451 Tm
94 Tz
(tstop\)) Tj
100 Tz
1 0 0 1 116 427 Tm
96 Tz
(Real) Tj
100 Tz
1 0 0 1 151 427 Tm
103 Tz
(tO,UO\(nxmk,nu\)) Tj
100 Tz
1 0 0 1 243 427 Tm
98 Tz
(,VO\(nv\)) Tj
100 Tz
/F11 11 Tf
1 0 0 1 290 427 Tm
50 Tz
(,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 296 427 Tm
67 Tz
(tI) Tj
100 Tz
1 0 0 1 309 427 Tm
78 Tz
(,UI) Tj
100 Tz
1 0 0 1 329 427 Tm
(\(nxmk,nu\)) Tj
1 0 0 1 388 427 Tm
78 Tz
(,VI) Tj
100 Tz
1 0 0 1 408 427 Tm
88 Tz
(\(nv\)) Tj
100 Tz
1 0 0 1 435 427 Tm
(~X\(nx\)) Tj
1 0 0 1 474 427 Tm
88 Tz
(,dt,) Tj
100 Tz
1 0 0 1 501 427 Tm
97 Tz
(tstop) Tj
100 Tz
1 0 0 1 116 403 Tm
96 Tz
(Real) Tj
100 Tz
1 0 0 1 150 403 Tm
104 Tz
(xe\(3\),Ue\(3\)) Tj
100 Tz
1 0 0 1 118 379 Tm
83 Tz
(If) Tj
100 Tz
1 0 0 1 137 379 Tm
33 Tz
(\() Tj
100 Tz
1 0 0 1 151 379 Tm
75 Tz
(tO) Tj
100 Tz
1 0 0 1 190 379 Tm
67 Tz
(ti) Tj
100 Tz
1 0 0 1 210 379 Tm
33 Tz
(\)) Tj
100 Tz
/F10 13 Tf
1 0 0 1 224 379 Tm
25 Tz
(\() Tj
100 Tz
/F1 10 Tf
1 0 0 1 235 379 Tm
103 Tz
(Return) Tj
100 Tz
/F10 13 Tf
1 0 0 1 283 379 Tm
20 Tz
(I) Tj
100 Tz
/F1 10 Tf
1 0 0 1 117 354 Tm
97 Tz
(xe\(1\)) Tj
100 Tz
1 0 0 1 171 354 Tm
104 Tz
(1.OeO/3.OeO) Tj
100 Tz
1 0 0 1 262 354 Tm
97 Tz
(xe\(2\)) Tj
100 Tz
1 0 0 1 314 354 Tm
103 Tz
(O.5e0) Tj
100 Tz
1 0 0 1 367 354 Tm
97 Tz
(xe\(3\)) Tj
100 Tz
1 0 0 1 420 354 Tm
106 Tz
(2.OeO/3.OeO) Tj
100 Tz
1 0 0 1 115 331 Tm
(Call) Tj
1 0 0 1 149 331 Tm
99 Tz
(Spl\202ne\(k,X,nx,Ul) Tj
100 Tz
1 0 0 1 250 331 Tm
(,xe,3,Ue\)) Tj
0 g
1 g
/F1 10 Tf
1 0 0 1 114 307 Tm
(Wr) Tj
1 0 0 1 132 307 Tm
17 Tz
(i) Tj
100 Tz
1 0 0 1 138 307 Tm
83 Tz
(te\() Tj
100 Tz
1 0 0 1 158 307 Tm
17 Tz
(I) Tj
100 Tz
1 0 0 1 164 307 Tm
(lmach\(2\)) Tj
1 0 0 1 217 307 Tm
94 Tz
(,9000\)) Tj
100 Tz
/F2 8 Tf
1 0 0 1 263 307 Tm
50 Tz
(t) Tj
100 Tz
/F1 10 Tf
1 0 0 1 269 307 Tm
67 Tz
(I,) Tj
100 Tz
1 0 0 1 282 307 Tm
92 Tz
(\(Ue\() Tj
100 Tz
1 0 0 1 117 295 Tm
(9000) Tj
1 0 0 1 150 295 Tm
110 Tz
(Format\(\204U\(x,\204,lple9.2,\204) Tj
100 Tz
0 g
1 g
/F10 11 Tf
1 0 0 1 315 306 Tm
67 Tz
(\)) Tj
100 Tz
/F10 5 Tf
1 0 0 1 322 306 Tm
171 Tz
(,i=l,3\)) Tj
100 Tz
/F10 11 Tf
1 0 0 1 315 295 Tm
67 Tz
(\)) Tj
100 Tz
/F5 4 Tf
1 0 0 1 326 295 Tm
173 Tz
(=\203) Tj
100 Tz
/F11 11 Tf
1 0 0 1 342 295 Tm
50 Tz
(,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 348 295 Tm
130 Tz
(lp3eIO.2\)) Tj
100 Tz
0 g
1 g
/F1 10 Tf
1 0 0 1 117 271 Tm
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(Re) Tj
100 Tz
1 0 0 1 132 271 Tm
92 Tz
(turn) Tj
100 Tz
1 0 0 1 117 247 Tm
(End) Tj
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89 Tz
(The) Tj
100 Tz
1 0 0 1 124 226 Tm
75 Tz
(output) Tj
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1 0 0 1 156 226 Tm
75 Tz
(of) Tj
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1 0 0 1 169 226 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 186 226 Tm
80 Tz
(above) Tj
100 Tz
1 0 0 1 215 226 Tm
83 Tz
(program) Tj
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1 0 0 1 255 226 Tm
42 Tz
(is) Tj
100 Tz
0 g
1 g
/F9 11 Tf
1 0 0 1 145 208 Tm
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(1) Tj
100 Tz
1 0 0 1 152 208 Tm
105 Tz
(.OOE-06) Tj
100 Tz
/F1 10 Tf
1 0 0 1 144 196 Tm
67 Tz
(7.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 157 196 Tm
103 Tz
(38E-04) Tj
100 Tz
1 0 0 1 157 184 Tm
97 Tz
(58E-01) Tj
100 Tz
1 0 0 1 144 172 Tm
67 Tz
(6.) Tj
100 Tz
1 0 0 1 157 172 Tm
97 Tz
(20E-0l) Tj
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1 0 0 1 157 161 Tm
(OOE) Tj
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92 Tz
(00) Tj
100 Tz
0 g
1 g
/F5 5 Tf
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171 Tz
(=) Tj
100 Tz
/F1 10 Tf
1 0 0 1 237 208 Tm
(1.OOE) Tj
1 0 0 1 203 196 Tm
33 Tz
(\)) Tj
100 Tz
1 0 0 1 237 196 Tm
(1.OOE) Tj
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33 Tz
(\)) Tj
100 Tz
/F5 5 Tf
1 0 0 1 214 184 Tm
171 Tz
(=) Tj
100 Tz
/F1 10 Tf
1 0 0 1 237 184 Tm
120 Tz
(lOSE) Tj
100 Tz
/F5 5 Tf
1 0 0 1 214 172 Tm
171 Tz
(=) Tj
100 Tz
/F9 11 Tf
1 0 0 1 237 172 Tm
123 Tz
(l.23E) Tj
100 Tz
/F10 11 Tf
1 0 0 1 203 160 Tm
67 Tz
(\)) Tj
100 Tz
/F5 5 Tf
1 0 0 1 215 160 Tm
171 Tz
(=) Tj
100 Tz
/F9 11 Tf
1 0 0 1 237 160 Tm
117 Tz
(1.40E) Tj
100 Tz
0 g
1 g
/F1 10 Tf
1 0 0 1 275 208 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 275 196 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 275 184 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 275 172 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 275 160 Tm
92 Tz
(00) Tj
100 Tz
0 g
1 g
/F10 5 Tf
1 0 0 1 303 208 Tm
(I) Tj
1 0 0 1 309 208 Tm
(.) Tj
1 0 0 1 314 208 Tm
139 Tz
(OOE) Tj
100 Tz
/F9 11 Tf
1 0 0 1 314 196 Tm
82 Tz
(OGE) Tj
100 Tz
1 0 0 1 314 184 Tm
106 Tz
(08E) Tj
100 Tz
/F10 11 Tf
1 0 0 1 303 172 Tm
(1.) Tj
/F10 5 Tf
1 0 0 1 315 172 Tm
156 Tz
(37E) Tj
100 Tz
/F9 10 Tf
1 0 0 1 314 160 Tm
111 Tz
(6SF) Tj
100 Tz
0 g
1 g
/F1 10 Tf
1 0 0 1 341 208 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 341 196 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 341 184 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 341 172 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 341 160 Tm
92 Tz
(00) Tj
100 Tz
0 g
1 g
/F9 11 Tf
1 0 0 1 380 208 Tm
82 Tz
(OOE) Tj
100 Tz
/F10 5 Tf
1 0 0 1 375 196 Tm
(\206) Tj
1 0 0 1 380 196 Tm
139 Tz
(OGE) Tj
100 Tz
/F1 10 Tf
1 0 0 1 368 184 Tm
83 Tz
(1.1) Tj
100 Tz
1 0 0 1 388 184 Tm
83 Tz
(IE) Tj
100 Tz
1 0 0 1 368 172 Tm
67 Tz
(1.) Tj
100 Tz
1 0 0 1 381 172 Tm
(52E) Tj
1 0 0 1 380 160 Tm
(95E) Tj
0 g
1 g
/F1 10 Tf
1 0 0 1 407 208 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 407 196 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 407 184 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 407 172 Tm
92 Tz
(00) Tj
100 Tz
1 0 0 1 407 160 Tm
92 Tz
(00) Tj
100 Tz
0 g
1 g
/F9 10 Tf
1 0 0 1 104 139 Tm
86 Tz
(A) Tj
100 Tz
1 0 0 1 115 139 Tm
103 Tz
(skeptic) Tj
100 Tz
1 0 0 1 149 139 Tm
104 Tz
(might) Tj
100 Tz
1 0 0 1 178 139 Tm
106 Tz
(observe) Tj
100 Tz
1 0 0 1 216 139 Tm
(that) Tj
1 0 0 1 236 139 Tm
(it) Tj
1 0 0 1 246 139 Tm
(is) Tj
1 0 0 1 256 139 Tm
(difficult) Tj
1 0 0 1 293 139 Tm
(to) Tj
1 0 0 1 305 139 Tm
109 Tz
(determine) Tj
100 Tz
1 0 0 1 353 139 Tm
106 Tz
(that) Tj
100 Tz
1 0 0 1 374 139 Tm
(the) Tj
1 0 0 1 391 139 Tm
108 Tz
(above) Tj
100 Tz
1 0 0 1 420 139 Tm
107 Tz
(output) Tj
100 Tz
1 0 0 1 452 139 Tm
(is) Tj
1 0 0 1 463 139 Tm
(in) Tj
1 0 0 1 475 139 Tm
(fact) Tj
1 0 0 1 493 139 Tm
106 Tz
(accurate) Tj
100 Tz
/F1 10 Tf
1 0 0 1 104 127 Tm
58 Tz
(to) Tj
100 Tz
/F1 10 Tf
1 0 0 1 117 127 Tm
54 Tz
(I/o.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 138 127 Tm
105 Tz
(Well,) Tj
100 Tz
1 0 0 1 165 127 Tm
105 Tz
(since) Tj
100 Tz
1 0 0 1 191 127 Tm
(the) Tj
1 0 0 1 208 127 Tm
105 Tz
(exact) Tj
100 Tz
1 0 0 1 235 127 Tm
94 Tz
(solu\204tion) Tj
100 Tz
1 0 0 1 273 127 Tm
111 Tz
(of) Tj
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1 0 0 1 286 127 Tm
(the) Tj
1 0 0 1 303 127 Tm
106 Tz
(problem) Tj
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1 0 0 1 343 127 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 352 127 Tm
106 Tz
(known,) Tj
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1 0 0 1 389 127 Tm
(the) Tj
1 0 0 1 406 127 Tm
106 Tz
(program) Tj
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1 0 0 1 446 127 Tm
94 Tz
(may) Tj
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1 0 0 1 467 127 Tm
(also) Tj
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(check) Tj
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1 0 0 1 515 127 Tm
(the) Tj
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(accuracy) Tj
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(of) Tj
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(the) Tj
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(numerical) Tj
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(solution) Tj
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(using) Tj
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(the) Tj
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104 Tz
(PORT) Tj
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/F9 10 Tf
1 0 0 1 335 115 Tm
(\[231) Tj
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93 Tz
(library) Tj
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1 0 0 1 388 115 Tm
(subroutine) Tj
1 0 0 1 439 115 Tm
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(Eesff) Tj
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1 0 0 1 464 115 Tm
88 Tz
(to) Tj
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1 0 0 1 475 115 Tm
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(estimate) Tj
100 Tz
1 0 0 1 515 115 Tm
92 Tz
(the) Tj
100 Tz
/F9 10 Tf
1 0 0 1 104 103 Tm
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(error) Tj
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/F5 14 Tf
1 0 0 1 130 103 Tm
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(Iju\205i~ii) Tj
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/F1 10 Tf
1 0 0 1 169 103 Tm
58 Tz
(in) Tj
100 Tz
1 0 0 1 180 103 Tm
67 Tz
(the) Tj
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1 0 0 1 197 103 Tm
88 Tz
(computed) Tj
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/F9 10 Tf
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106 Tz
(solution) Tj
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/F10 7 Tf
1 0 0 1 283 103 Tm
(t~.) Tj
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1 0 0 1 299 103 Tm
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(By) Tj
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(changing) Tj
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(the) Tj
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(body) Tj
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(of) Tj
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(Handle) Tj
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(to) Tj
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/F1 10 Tf
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(U\(X,) Tj
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(U\(X.) Tj
100 Tz
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104 Tz
(U\(X,) Tj
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/F1 10 Tf
1 0 0 1 110 172 Tm
96 Tz
(U\(X,) Tj
100 Tz
/F9 11 Tf
1 0 0 1 110 160 Tm
104 Tz
(U\(X,) Tj
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ET
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(error) Tj
100 Tz
1 0 0 1 153 697 Tm
104 Tz
(states) Tj
100 Tz
1 0 0 1 181 697 Tm
(flagged) Tj
1 0 0 1 216 697 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 231 697 Tm
(an) Tj
/F5 4 Tf
1 0 0 1 246 697 Tm
167 Tz
(*) Tj
100 Tz
/F9 10 Tf
1 0 0 1 254 697 Tm
107 Tz
(can) Tj
100 Tz
1 0 0 1 273 697 Tm
104 Tz
(occur) Tj
100 Tz
/F11 10 Tf
1 0 0 1 302 697 Tm
94 Tz
(only) Tj
100 Tz
/F9 10 Tf
1 0 0 1 323 697 Tm
(\\~hen) Tj
1 0 0 1 351 697 Tm
(POST) Tj
1 0 0 1 381 697 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 392 697 Tm
109 Tz
(entered) Tj
100 Tz
1 0 0 1 429 697 Tm
(at) Tj
1 0 0 1 442 697 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 451 697 Tm
(level) Tj
1 0 0 1 476 697 Tm
(below) Tj
1 0 0 1 506 697 Tm
104 Tz
(Posts.) Tj
100 Tz
1 0 0 1 105 685 Tm
(they) Tj
1 0 0 1 127 685 Tm
107 Tz
(cannot) Tj
100 Tz
1 0 0 1 160 685 Tm
104 Tz
(occur) Tj
100 Tz
1 0 0 1 187 685 Tm
105 Tz
(when) Tj
100 Tz
1 0 0 1 214 685 Tm
(Posts) Tj
1 0 0 1 241 685 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 251 685 Tm
106 Tz
(invoked.) Tj
100 Tz
1 0 0 1 112 670 Tm
33 Tz
(I) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 670 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 150 670 Tm
115 Tz
(nu\<0.) Tj
100 Tz
1 0 0 1 111 654 Tm
60 Tz
(2) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 654 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 150 654 Tm
115 Tz
(nv\<0.) Tj
100 Tz
1 0 0 1 110 638 Tm
60 Tz
(3) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 638 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 150 638 Tm
131 Tz
(nuO\202nv.) Tj
100 Tz
1 0 0 1 110 623 Tm
80 Tz
(4) Tj
100 Tz
/F5 4 Tf
1 0 0 1 135 623 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 149 623 Tm
124 Tz
(nu\>Oandk\<2) Tj
100 Tz
/F1 10 Tf
1 0 0 1 110 607 Tm
50 Tz
(5) Tj
100 Tz
/F5 4 Tf
1 0 0 1 134 607 Tm
150 Tz
(-) Tj
100 Tz
/F1 10 Tf
1 0 0 1 150 607 Tm
102 Tz
(nu\>Oandnx\<2*k.) Tj
100 Tz
/F11 11 Tf
1 0 0 1 110 593 Tm
80 Tz
(6) Tj
100 Tz
/F5 4 Tf
1 0 0 1 134 593 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 150 593 Tm
126 Tz
(tstart+dttstart.) Tj
100 Tz
1 0 0 1 232 593 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 253 593 Tm
106 Tz
(user-chosen) Tj
100 Tz
1 0 0 1 309 593 Tm
(initial) Tj
1 0 0 1 337 593 Tm
105 Tz
(value) Tj
100 Tz
1 0 0 1 364 593 Tm
(for) Tj
1 0 0 1 381 593 Tm
(the) Tj
1 0 0 1 398 593 Tm
105 Tz
(tinle-step) Tj
100 Tz
1 0 0 1 442 593 Tm
112 Tz
(dt) Tj
100 Tz
1 0 0 1 455 593 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 465 593 Tm
(too) Tj
1 0 0 1 482 593 Tm
(small.) Tj
/F9 10 Tf
1 0 0 1 110 577 Tm
60 Tz
(7) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 577 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 148 577 Tm
89 Tz
(The) Tj
100 Tz
1 0 0 1 171 577 Tm
73 Tz
(input) Tj
100 Tz
1 0 0 1 199 577 Tm
73 Tz
(value) Tj
100 Tz
1 0 0 1 227 577 Tm
75 Tz
(of) Tj
100 Tz
1 0 0 1 241 577 Tm
58 Tz
(dt) Tj
100 Tz
1 0 0 1 255 577 Tm
72 Tz
(has) Tj
100 Tz
1 0 0 1 274 577 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 293 577 Tm
83 Tz
(wrong) Tj
100 Tz
1 0 0 1 325 577 Tm
60 Tz
(sign.) Tj
100 Tz
1 0 0 1 353 577 Tm
58 Tz
(dt) Tj
100 Tz
1 0 0 1 367 577 Tm
78 Tz
(and) Tj
100 Tz
1 0 0 1 387 577 Tm
64 Tz
(tstop-tstart) Tj
100 Tz
1 0 0 1 440 577 Tm
83 Tz
(must) Tj
100 Tz
1 0 0 1 466 577 Tm
79 Tz
(have) Tj
100 Tz
1 0 0 1 492 577 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 510 577 Tm
88 Tz
(same) Tj
100 Tz
/F9 10 Tf
1 0 0 1 149 565 Tm
95 Tz
(sign.) Tj
100 Tz
1 0 0 1 110 549 Tm
60 Tz
(8) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 549 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 149 549 Tm
83 Tz
(nxid\<0.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 110 534 Tm
67 Tz
(9*) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 534 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 149 534 Tm
114 Tz
(theta\<0) Tj
100 Tz
1 0 0 1 190 534 Tm
(or) Tj
1 0 0 1 202 534 Tm
121 Tz
(theta\>l.) Tj
100 Tz
1 0 0 1 111 518 Tm
80 Tz
(10*) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 518 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 149 518 Tm
103 Tz
(Keepjac) Tj
100 Tz
1 0 0 1 187 518 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 205 518 Tm
107 Tz
(one) Tj
100 Tz
1 0 0 1 224 518 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 238 518 Tm
106 Tz
(\(0,1.2\).) Tj
100 Tz
1 0 0 1 111 502 Tm
80 Tz
(11*) Tj
100 Tz
/F5 4 Tf
1 0 0 1 134 502 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 149 502 Tm
118 Tz
(miter\<l.) Tj
100 Tz
1 0 0 1 111 487 Tm
80 Tz
(12*) Tj
100 Tz
/F5 4 Tf
1 0 0 1 134 487 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 149 487 Tm
117 Tz
(mgq\<I.) Tj
100 Tz
1 0 0 1 111 472 Tm
80 Tz
(13*) Tj
100 Tz
/F5 4 Tf
1 0 0 1 134 472 Tm
150 Tz
(-) Tj
100 Tz
/F1 10 Tf
1 0 0 1 149 472 Tm
95 Tz
(kmax\<1.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 111 456 Tm
80 Tz
(14*) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 456 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 149 456 Tm
75 Tz
(kinit\<l.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 111 441 Tm
(IS) Tj
/F10 7 Tf
1 0 0 1 134 441 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 150 441 Tm
58 Tz
(x\() Tj
100 Tz
1 0 0 1 160 441 Tm
50 Tz
(1\)) Tj
100 Tz
1 0 0 1 173 441 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 182 441 Tm
72 Tz
(not) Tj
100 Tz
1 0 0 1 200 441 Tm
75 Tz
(of) Tj
100 Tz
1 0 0 1 213 441 Tm
67 Tz
(multiplicity) Tj
100 Tz
1 0 0 1 266 441 Tm
50 Tz
(k.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 111 426 Tm
80 Tz
(16) Tj
100 Tz
/F5 4 Tf
1 0 0 1 135 426 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 150 426 Tm
109 Tz
(x\(nx\)) Tj
100 Tz
1 0 0 1 178 426 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 189 426 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 206 426 Tm
(of) Tj
1 0 0 1 219 426 Tm
104 Tz
(multiplicity) Tj
100 Tz
1 0 0 1 272 426 Tm
86 Tz
(k.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 111 410 Tm
80 Tz
(17) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 410 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 150 410 Tm
67 Tz
(x) Tj
100 Tz
1 0 0 1 158 410 Tm
50 Tz
(is) Tj
100 Tz
1 0 0 1 169 410 Tm
72 Tz
(not) Tj
100 Tz
/F9 10 Tf
1 0 0 1 186 410 Tm
107 Tz
(monotone) Tj
100 Tz
1 0 0 1 235 410 Tm
104 Tz
(increasing.) Tj
100 Tz
1 0 0 1 111 395 Tm
80 Tz
(18) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 395 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 149 395 Tm
110 Tz
(Cannot) Tj
100 Tz
1 0 0 1 185 395 Tm
105 Tz
(have) Tj
100 Tz
/F1 10 Tf
1 0 0 1 209 395 Tm
92 Tz
(nxid\>0) Tj
100 Tz
1 0 0 1 246 395 Tm
83 Tz
(and) Tj
100 Tz
1 0 0 1 266 395 Tm
111 Tz
(nuO.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 111 379 Tm
80 Tz
(19) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 379 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 149 379 Tm
110 Tz
(Cannot) Tj
100 Tz
1 0 0 1 185 379 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 209 379 Tm
115 Tz
(nxid\>0) Tj
100 Tz
1 0 0 1 246 379 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 266 379 Tm
130 Tz
(nvO.) Tj
100 Tz
1 0 0 1 110 363 Tm
90 Tz
(20) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 363 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 149 363 Tm
132 Tz
(dtO.) Tj
100 Tz
1 0 0 1 182 363 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 255 363 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 278 363 Tm
105 Tz
(time-step) Tj
100 Tz
1 0 0 1 324 363 Tm
(has) Tj
1 0 0 1 344 363 Tm
103 Tz
(become) Tj
100 Tz
1 0 0 1 382 363 Tm
108 Tz
(too) Tj
100 Tz
1 0 0 1 401 363 Tm
(small.) Tj
1 0 0 1 435 363 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 458 363 Tm
106 Tz
(problem) Tj
100 Tz
1 0 0 1 500 363 Tm
94 Tz
(may) Tj
100 Tz
1 0 0 1 522 363 Tm
(be) Tj
1 0 0 1 150 351 Tm
(very) Tj
1 0 0 1 173 351 Tm
95 Tz
(badly) Tj
100 Tz
1 0 0 1 199 351 Tm
(scaled,) Tj
1 0 0 1 233 351 Tm
(that) Tj
1 0 0 1 253 351 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 264 351 Tm
110 Tz
(units) Tj
100 Tz
1 0 0 1 290 351 Tm
93 Tz
(like) Tj
100 Tz
1 0 0 1 309 351 Tm
105 Tz
(light-years) Tj
100 Tz
1 0 0 1 358 351 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 378 351 Tm
106 Tz
(micro-grams) Tj
100 Tz
1 0 0 1 436 351 Tm
(are) Tj
1 0 0 1 454 351 Tm
(being) Tj
1 0 0 1 481 351 Tm
105 Tz
(used) Tj
100 Tz
1 0 0 1 505 351 Tm
115 Tz
(simul) Tj
100 Tz
(-) Tj
1 0 0 1 150 339 Tm
105 Tz
(taneously.) Tj
100 Tz
1 0 0 1 203 339 Tm
109 Tz
(Another) Tj
100 Tz
1 0 0 1 245 339 Tm
104 Tz
(cause) Tj
100 Tz
1 0 0 1 275 339 Tm
(is) Tj
1 0 0 1 287 339 Tm
(too) Tj
1 0 0 1 306 339 Tm
105 Tz
(small) Tj
100 Tz
1 0 0 1 335 339 Tm
(an) Tj
1 0 0 1 350 339 Tm
103 Tz
(accuracy) Tj
100 Tz
1 0 0 1 393 339 Tm
109 Tz
(requirement,) Tj
100 Tz
1 0 0 1 456 339 Tm
93 Tz
(like) Tj
100 Tz
1 0 0 1 477 339 Tm
108 Tz
(errpar\(2\)) Tj
100 Tz
1 0 0 1 518 339 Tm
117 Tz
(=0) Tj
100 Tz
1 0 0 1 149 328 Tm
105 Tz
(when) Tj
100 Tz
1 0 0 1 176 328 Tm
(the) Tj
1 0 0 1 193 328 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 233 328 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 242 328 Tm
104 Tz
(exceedingly) Tj
100 Tz
1 0 0 1 297 328 Tm
(small.) Tj
1 0 0 1 110 312 Tm
80 Tz
(21) Tj
100 Tz
/F5 4 Tf
1 0 0 1 135 312 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 149 312 Tm
122 Tz
(dt=0) Tj
100 Tz
1 0 0 1 179 312 Tm
108 Tz
(returned) Tj
100 Tz
1 0 0 1 223 312 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 239 312 Tm
109 Tz
(handle.) Tj
100 Tz
1 0 0 1 280 312 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 355 312 Tm
103 Tz
(Handle) Tj
100 Tz
1 0 0 1 392 312 Tm
103 Tz
(lowered) Tj
100 Tz
1 0 0 1 432 312 Tm
(dt) Tj
1 0 0 1 446 312 Tm
(and) Tj
1 0 0 1 468 312 Tm
80 Tz
(it) Tj
100 Tz
1 0 0 1 480 312 Tm
103 Tz
(became) Tj
100 Tz
1 0 0 1 519 312 Tm
(too) Tj
1 0 0 1 150 299 Tm
(small.) Tj
1 0 0 1 110 285 Tm
80 Tz
(22) Tj
100 Tz
/F10 7 Tf
1 0 0 1 134 285 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 149 285 Tm
112 Tz
(dt) Tj
100 Tz
1 0 0 1 161 285 Tm
108 Tz
(returned) Tj
100 Tz
1 0 0 1 203 285 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 216 285 Tm
107 Tz
(Handle) Tj
100 Tz
1 0 0 1 251 285 Tm
(has) Tj
1 0 0 1 269 285 Tm
(the) Tj
1 0 0 1 286 285 Tm
104 Tz
(wrong) Tj
100 Tz
1 0 0 1 317 285 Tm
95 Tz
(sign.) Tj
100 Tz
1 0 0 1 341 285 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 110 269 Tm
87 Tz
(23*) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 269 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 149 269 Tm
110 Tz
(Cannot) Tj
100 Tz
1 0 0 1 185 269 Tm
(raise) Tj
1 0 0 1 208 269 Tm
(dt) Tj
1 0 0 1 221 269 Tm
(in) Tj
1 0 0 1 233 269 Tm
107 Tz
(Handle) Tj
100 Tz
1 0 0 1 267 269 Tm
105 Tz
(when) Tj
100 Tz
1 0 0 1 294 269 Tm
(Failed.) Tj
1 0 0 1 328 269 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 110 254 Tm
90 Tz
(24) Tj
100 Tz
/F5 4 Tf
1 0 0 1 135 254 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 149 254 Tm
107 Tz
(e\(i\)) Tj
100 Tz
/F10 7 Tf
1 0 0 1 167 254 Tm
150 Tz
(\<) Tj
100 Tz
/F9 10 Tf
1 0 0 1 177 254 Tm
123 Tz
(=0) Tj
100 Tz
1 0 0 1 195 254 Tm
108 Tz
(returned) Tj
100 Tz
1 0 0 1 236 254 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 250 254 Tm
104 Tz
(Error.) Tj
100 Tz
1 0 0 1 280 254 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 351 254 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 372 254 Tm
110 Tz
(error) Tj
100 Tz
1 0 0 1 398 254 Tm
110 Tz
(request) Tj
100 Tz
1 0 0 1 433 254 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 443 254 Tm
(too) Tj
1 0 0 1 461 254 Tm
(small.) Tj
1 0 0 1 110 238 Tm
80 Tz
(25) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 238 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 150 238 Tm
105 Tz
(Dirichlet) Tj
100 Tz
1 0 0 1 195 238 Tm
95 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 221 238 Tm
(are) Tj
1 0 0 1 240 238 Tm
108 Tz
(overdetermined.) Tj
100 Tz
1 0 0 1 319 238 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 393 238 Tm
108 Tz
(There) Tj
100 Tz
1 0 0 1 425 238 Tm
(are) Tj
1 0 0 1 445 238 Tm
(too) Tj
1 0 0 1 464 238 Tm
(many) Tj
1 0 0 1 494 238 Tm
105 Tz
(Dirichlet) Tj
100 Tz
/F1 10 Tf
1 0 0 1 150 227 Tm
73 Tz
(BC\202s.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 110 211 Tm
75 Tz
(26) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 211 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 150 211 Tm
90 Tz
(Mixed) Tj
100 Tz
/F9 10 Tf
1 0 0 1 181 211 Tm
95 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 205 211 Tm
(are) Tj
1 0 0 1 222 211 Tm
108 Tz
(overdetermined.) Tj
100 Tz
1 0 0 1 298 211 Tm
108 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 370 211 Tm
108 Tz
(There) Tj
100 Tz
1 0 0 1 400 211 Tm
(are) Tj
1 0 0 1 417 211 Tm
(too) Tj
1 0 0 1 435 211 Tm
(many) Tj
1 0 0 1 461 211 Tm
104 Tz
(mixed) Tj
100 Tz
1 0 0 1 492 211 Tm
91 Tz
(BC\202s.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 110 196 Tm
80 Tz
(27) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 196 Tm
(-) Tj
/F9 10 Tf
1 0 0 1 150 196 Tm
107 Tz
(Improper) Tj
100 Tz
1 0 0 1 195 196 Tm
96 Tz
(BC\202s.) Tj
100 Tz
1 0 0 1 223 196 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 295 196 Tm
106 Tz
(The) Tj
100 Tz
/F9 10 Tf
1 0 0 1 317 196 Tm
(BC\202s) Tj
1 0 0 1 341 196 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 362 196 Tm
(the) Tj
1 0 0 1 380 196 Tm
104 Tz
(PDE\202s) Tj
100 Tz
1 0 0 1 412 196 Tm
(do) Tj
1 0 0 1 427 196 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 445 196 Tm
104 Tz
(match) Tj
100 Tz
1 0 0 1 476 196 Tm
103 Tz
(properly.) Tj
100 Tz
1 0 0 1 519 196 Tm
(see) Tj
/F9 10 Tf
1 0 0 1 150 183 Tm
103 Tz
(section) Tj
100 Tz
1 0 0 1 184 183 Tm
86 Tz
(9.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 110 168 Tm
75 Tz
(28) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 168 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 149 168 Tm
89 Tz
(Too) Tj
100 Tz
1 0 0 1 171 168 Tm
78 Tz
(few) Tj
100 Tz
1 0 0 1 189 168 Tm
73 Tz
(BC\202s.) Tj
100 Tz
1 0 0 1 217 168 Tm
75 Tz
(\(Recoverable\).) Tj
100 Tz
/F9 10 Tf
1 0 0 1 110 152 Tm
90 Tz
(29) Tj
100 Tz
/F5 4 Tf
1 0 0 1 135 152 Tm
150 Tz
(-) Tj
100 Tz
/F1 10 Tf
1 0 0 1 149 152 Tm
89 Tz
(Too) Tj
100 Tz
1 0 0 1 171 152 Tm
92 Tz
(many) Tj
100 Tz
1 0 0 1 198 152 Tm
73 Tz
(BC\202s.) Tj
100 Tz
1 0 0 1 225 152 Tm
75 Tz
(\(Recoverable\).) Tj
100 Tz
/F9 10 Tf
1 0 0 1 110 137 Tm
90 Tz
(30) Tj
100 Tz
/F10 7 Tf
1 0 0 1 135 137 Tm
(-) Tj
/F1 10 Tf
1 0 0 1 150 137 Tm
79 Tz
(lxid\<0.) Tj
100 Tz
1 0 0 1 188 137 Tm
75 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 260 137 Tm
79 Tz
(User) Tj
100 Tz
1 0 0 1 284 137 Tm
73 Tz
(supplied) Tj
100 Tz
1 0 0 1 324 137 Tm
77 Tz
(subroutine) Tj
100 Tz
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1 0 0 1 134 558 Tm
150 Tz
(-) Tj
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1 0 0 1 148 558 Tm
108 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 190 558 Tm
105 Tz
(coefficient) Tj
100 Tz
1 0 0 1 238 558 Tm
111 Tz
(of) Tj
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/F11 10 Tf
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(u~) Tj
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(changes) Tj
100 Tz
1 0 0 1 306 558 Tm
95 Tz
(sign.) Tj
100 Tz
1 0 0 1 331 558 Tm
106 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 403 558 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 424 558 Tm
105 Tz
(linearized) Tj
100 Tz
1 0 0 1 470 558 Tm
106 Tz
(problem) Tj
100 Tz
1 0 0 1 510 558 Tm
92 Tz
(has) Tj
100 Tz
1 0 0 1 527 558 Tm
75 Tz
(a) Tj
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94 Tz
(singular) Tj
100 Tz
1 0 0 1 187 545 Tm
97 Tz
(solution,) Tj
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1 0 0 1 229 545 Tm
96 Tz
(which) Tj
100 Tz
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93 Tz
(forced) Tj
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108 Tz
(dt=0.) Tj
100 Tz
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81 Tz
(43*) Tj
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(-) Tj
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1 0 0 1 148 532 Tm
(Too) Tj
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(many) Tj
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(Newton) Tj
100 Tz
1 0 0 1 236 532 Tm
(iterations) Tj
1 0 0 1 280 532 Tm
95 Tz
(required.) Tj
100 Tz
1 0 0 1 324 532 Tm
97 Tz
(\(Recoverable\).) Tj
100 Tz
1 0 0 1 396 532 Tm
94 Tz
(The) Tj
100 Tz
1 0 0 1 418 532 Tm
98 Tz
(nonlinear) Tj
100 Tz
1 0 0 1 462 532 Tm
98 Tz
(equations) Tj
100 Tz
1 0 0 1 508 532 Tm
96 Tz
(could) Tj
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(not) Tj
100 Tz
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89 Tz
(be) Tj
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107 Tz
(solved,) Tj
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1 0 0 1 217 518 Tm
104 Tz
(which) Tj
100 Tz
1 0 0 1 247 518 Tm
104 Tz
(forced) Tj
100 Tz
1 0 0 1 278 518 Tm
109 Tz
(dt~0.) Tj
100 Tz
1 0 0 1 310 518 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 331 518 Tm
108 Tz
(user\202s) Tj
100 Tz
1 0 0 1 361 518 Tm
107 Tz
(computation) Tj
100 Tz
1 0 0 1 420 518 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 433 518 Tm
(the) Tj
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106 Tz
(Jacobian) Tj
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104 Tz
(values) Tj
100 Tz
1 0 0 1 524 518 Tm
86 Tz
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(AF,) Tj
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(B) Tj
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(or) Tj
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86 Tz
(D) Tj
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(be) Tj
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(incorrect.) Tj
100 Tz
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109 Tz
(Another) Tj
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(cause) Tj
100 Tz
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(of) Tj
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107 Tz
(this) Tj
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1 0 0 1 393 506 Tm
106 Tz
(problem) Tj
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104 Tz
(could) Tj
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89 Tz
(be) Tj
100 Tz
1 0 0 1 476 506 Tm
102 Tz
(insufficiently) Tj
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71 Tz
(accurate) Tj
100 Tz
1 0 0 1 188 493 Tm
82 Tz
(computation) Tj
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(of) Tj
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(the) Tj
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(Jacobian) Tj
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(values) Tj
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(or) Tj
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(values) Tj
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(a) Tj
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(f.) Tj
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/F1 10 Tf
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(8.) Tj
100 Tz
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1 0 0 1 119 470 Tm
92 Tz
(Time) Tj
100 Tz
1 0 0 1 146 470 Tm
96 Tz
(Discretization.) Tj
100 Tz
/F9 10 Tf
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86 Tz
(A) Tj
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1 0 0 1 142 455 Tm
108 Tz
(one-step,) Tj
100 Tz
1 0 0 1 188 455 Tm
(implicit) Tj
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(finite) Tj
1 0 0 1 253 455 Tm
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(difference) Tj
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1 0 0 1 301 455 Tm
106 Tz
(method) Tj
100 Tz
1 0 0 1 340 455 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 351 455 Tm
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(employed) Tj
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1 0 0 1 399 455 Tm
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(for) Tj
100 Tz
1 0 0 1 417 455 Tm
(the) Tj
1 0 0 1 435 455 Tm
106 Tz
(time) Tj
100 Tz
1 0 0 1 459 455 Tm
107 Tz
(discretization) Tj
100 Tz
1 0 0 1 522 455 Tm
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(of) Tj
100 Tz
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93 Tz
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(\)-\(5.3\).) Tj
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(The) Tj
100 Tz
1 0 0 1 185 442 Tm
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(resulting) Tj
100 Tz
1 0 0 1 228 442 Tm
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(nonlinear) Tj
100 Tz
1 0 0 1 273 442 Tm
107 Tz
(ODE\202s) Tj
100 Tz
1 0 0 1 308 442 Tm
(in) Tj
1 0 0 1 321 442 Tm
(space) Tj
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(are) Tj
1 0 0 1 367 442 Tm
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(then) Tj
100 Tz
1 0 0 1 391 442 Tm
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(linearized,) Tj
100 Tz
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(the) Tj
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(BC\202s) Tj
100 Tz
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(and) Tj
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(the) Tj
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(original) Tj
100 Tz
1 0 0 1 159 430 Tm
103 Tz
(ODE\202s.) Tj
100 Tz
1 0 0 1 200 430 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 222 430 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 261 430 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 275 430 Tm
(the) Tj
1 0 0 1 292 430 Tm
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(resulting) Tj
100 Tz
1 0 0 1 335 430 Tm
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(system) Tj
100 Tz
1 0 0 1 369 430 Tm
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(of) Tj
100 Tz
1 0 0 1 383 430 Tm
104 Tz
(linear) Tj
100 Tz
1 0 0 1 411 430 Tm
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(ODE\202s) Tj
100 Tz
1 0 0 1 445 430 Tm
(in) Tj
1 0 0 1 458 430 Tm
104 Tz
(space,) Tj
100 Tz
1 0 0 1 488 430 Tm
103 Tz
(subject) Tj
100 Tz
1 0 0 1 524 430 Tm
(to) Tj
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(linear) Tj
100 Tz
1 0 0 1 134 418 Tm
96 Tz
(BC\202s,) Tj
100 Tz
1 0 0 1 163 418 Tm
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(with) Tj
100 Tz
1 0 0 1 187 418 Tm
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(coupled) Tj
100 Tz
1 0 0 1 227 418 Tm
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(linear) Tj
100 Tz
1 0 0 1 257 418 Tm
103 Tz
(algebraic) Tj
100 Tz
1 0 0 1 301 418 Tm
109 Tz
(equations.) Tj
100 Tz
1 0 0 1 352 418 Tm
(is) Tj
1 0 0 1 364 418 Tm
107 Tz
(accomplished) Tj
100 Tz
1 0 0 1 428 418 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 443 418 Tm
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(Galerkin\202s) Tj
100 Tz
1 0 0 1 495 418 Tm
109 Tz
(method,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 406 Tm
105 Tz
(using) Tj
100 Tz
1 0 0 1 131 406 Tm
102 Tz
(B-splines,) Tj
100 Tz
1 0 0 1 177 406 Tm
(as) Tj
1 0 0 1 189 406 Tm
105 Tz
(described) Tj
100 Tz
1 0 0 1 234 406 Tm
(in) Tj
1 0 0 1 246 406 Tm
103 Tz
(section) Tj
100 Tz
1 0 0 1 280 406 Tm
86 Tz
(9.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 129 391 Tm
(An) Tj
1 0 0 1 146 391 Tm
107 Tz
(extrapolation) Tj
100 Tz
1 0 0 1 208 391 Tm
106 Tz
(scheme) Tj
100 Tz
1 0 0 1 246 391 Tm
(\(see) Tj
1 0 0 1 267 391 Tm
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(Appendix) Tj
100 Tz
1 0 0 1 314 391 Tm
88 Tz
(2\)) Tj
100 Tz
1 0 0 1 327 391 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 338 391 Tm
103 Tz
(applied) Tj
100 Tz
/F9 10 Tf
1 0 0 1 373 391 Tm
(to) Tj
1 0 0 1 386 391 Tm
(the) Tj
1 0 0 1 404 391 Tm
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(results) Tj
100 Tz
1 0 0 1 436 391 Tm
(of) Tj
1 0 0 1 449 391 Tm
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(this) Tj
100 Tz
1 0 0 1 468 391 Tm
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(one-step) Tj
100 Tz
1 0 0 1 509 391 Tm
(finite) Tj
1 0 0 1 104 379 Tm
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(difference) Tj
100 Tz
/F9 10 Tf
1 0 0 1 152 379 Tm
106 Tz
(method) Tj
100 Tz
/F1 10 Tf
1 0 0 1 189 379 Tm
58 Tz
(in) Tj
100 Tz
1 0 0 1 202 379 Tm
67 Tz
(time.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 231 379 Tm
111 Tz
(This) Tj
100 Tz
1 0 0 1 254 379 Tm
(allows) Tj
1 0 0 1 285 379 Tm
(an) Tj
1 0 0 1 299 379 Tm
107 Tz
(extrapolation) Tj
100 Tz
1 0 0 1 360 379 Tm
106 Tz
(step-size) Tj
100 Tz
1 0 0 1 402 379 Tm
107 Tz
(and) Tj
100 Tz
/F9 10 Tf
1 0 0 1 421 379 Tm
105 Tz
(order) Tj
100 Tz
1 0 0 1 448 379 Tm
109 Tz
(monitor) Tj
100 Tz
1 0 0 1 488 379 Tm
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1 0 0 1 509 379 Tm
(to) Tj
1 0 0 1 522 379 Tm
89 Tz
(be) Tj
100 Tz
/F9 10 Tf
1 0 0 1 104 366 Tm
107 Tz
(employed) Tj
100 Tz
1 0 0 1 151 366 Tm
(which) Tj
1 0 0 1 180 366 Tm
104 Tz
(dynamically) Tj
100 Tz
1 0 0 1 236 366 Tm
106 Tz
(changes) Tj
100 Tz
1 0 0 1 275 366 Tm
106 Tz
(both) Tj
100 Tz
1 0 0 1 299 366 Tm
(the) Tj
1 0 0 1 317 366 Tm
95 Tz
(local) Tj
100 Tz
1 0 0 1 341 366 Tm
106 Tz
(step-size) Tj
100 Tz
1 0 0 1 383 366 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 403 366 Tm
105 Tz
(order) Tj
100 Tz
1 0 0 1 430 366 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 443 366 Tm
(the) Tj
1 0 0 1 461 366 Tm
107 Tz
(time-integration) Tj
100 Tz
/F9 10 Tf
1 0 0 1 104 355 Tm
109 Tz
(scheme) Tj
100 Tz
1 0 0 1 141 355 Tm
(to) Tj
1 0 0 1 153 355 Tm
96 Tz
(satisfy) Tj
100 Tz
1 0 0 1 184 355 Tm
(the) Tj
1 0 0 1 201 355 Tm
104 Tz
(user\202s) Tj
100 Tz
1 0 0 1 230 355 Tm
110 Tz
(error) Tj
100 Tz
1 0 0 1 255 355 Tm
110 Tz
(request) Tj
100 Tz
1 0 0 1 291 355 Tm
(in) Tj
1 0 0 1 302 355 Tm
(a) Tj
1 0 0 1 311 355 Tm
104 Tz
(reasonably) Tj
100 Tz
1 0 0 1 360 355 Tm
103 Tz
(optimal) Tj
100 Tz
1 0 0 1 397 355 Tm
106 Tz
(fashion.) Tj
100 Tz
1 0 0 1 129 339 Tm
107 Tz
(Although) Tj
100 Tz
1 0 0 1 175 339 Tm
(this) Tj
1 0 0 1 194 339 Tm
107 Tz
(outline) Tj
100 Tz
1 0 0 1 228 339 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 241 339 Tm
(the) Tj
1 0 0 1 259 339 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 298 339 Tm
106 Tz
(process) Tj
100 Tz
1 0 0 1 333 339 Tm
106 Tz
(appears) Tj
100 Tz
1 0 0 1 370 339 Tm
(to) Tj
1 0 0 1 382 339 Tm
(be) Tj
1 0 0 1 397 339 Tm
108 Tz
(inconsistent) Tj
100 Tz
1 0 0 1 452 339 Tm
106 Tz
(with) Tj
100 Tz
1 0 0 1 476 339 Tm
(that) Tj
1 0 0 1 496 339 Tm
(given) Tj
1 0 0 1 524 339 Tm
(in) Tj
1 0 0 1 104 327 Tm
103 Tz
(section) Tj
100 Tz
/F9 11 Tf
1 0 0 1 139 327 Tm
88 Tz
(3,) Tj
100 Tz
1 0 0 1 151 327 Tm
95 Tz
(both) Tj
100 Tz
1 0 0 1 174 327 Tm
(outlines) Tj
1 0 0 1 213 327 Tm
97 Tz
(produce) Tj
100 Tz
1 0 0 1 252 327 Tm
92 Tz
(the) Tj
100 Tz
/F11 10 Tf
1 0 0 1 270 327 Tm
105 Tz
(same) Tj
100 Tz
/F9 10 Tf
1 0 0 1 294 327 Tm
107 Tz
(numerical) Tj
100 Tz
1 0 0 1 341 327 Tm
106 Tz
(solution.) Tj
100 Tz
1 0 0 1 386 327 Tm
(Spatial) Tj
1 0 0 1 418 327 Tm
107 Tz
(discretization) Tj
100 Tz
1 0 0 1 480 327 Tm
103 Tz
(followed) Tj
100 Tz
1 0 0 1 522 327 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 104 315 Tm
107 Tz
(discretization) Tj
100 Tz
1 0 0 1 168 315 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 184 315 Tm
(the) Tj
1 0 0 1 204 315 Tm
105 Tz
(resulting) Tj
100 Tz
1 0 0 1 248 315 Tm
107 Tz
(ODE\202s) Tj
100 Tz
1 0 0 1 284 315 Tm
(in) Tj
1 0 0 1 299 315 Tm
106 Tz
(time) Tj
100 Tz
1 0 0 1 324 315 Tm
105 Tz
(gives) Tj
100 Tz
1 0 0 1 352 315 Tm
(the) Tj
1 0 0 1 372 315 Tm
105 Tz
(same) Tj
100 Tz
1 0 0 1 401 315 Tm
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(mathematical) Tj
100 Tz
1 0 0 1 465 315 Tm
106 Tz
(formulation) Tj
100 Tz
1 0 0 1 523 315 Tm
88 Tz
(as) Tj
100 Tz
1 0 0 1 105 303 Tm
107 Tz
(discretization) Tj
100 Tz
1 0 0 1 168 303 Tm
(in) Tj
1 0 0 1 182 303 Tm
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(time) Tj
100 Tz
1 0 0 1 207 303 Tm
103 Tz
(followed) Tj
100 Tz
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(by) Tj
100 Tz
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(spatial) Tj
100 Tz
1 0 0 1 297 303 Tm
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(discretization.) Tj
100 Tz
1 0 0 1 367 303 Tm
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(For) Tj
100 Tz
1 0 0 1 387 303 Tm
105 Tz
(overview,) Tj
100 Tz
1 0 0 1 435 303 Tm
(the) Tj
1 0 0 1 454 303 Tm
107 Tz
(former) Tj
100 Tz
1 0 0 1 489 303 Tm
107 Tz
(outline) Tj
100 Tz
1 0 0 1 525 303 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 104 291 Tm
104 Tz
(conceptually) Tj
100 Tz
1 0 0 1 164 291 Tm
106 Tz
(simpler,) Tj
100 Tz
1 0 0 1 206 291 Tm
108 Tz
(however,) Tj
100 Tz
1 0 0 1 252 291 Tm
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(for) Tj
100 Tz
1 0 0 1 271 291 Tm
(the) Tj
1 0 0 1 290 291 Tm
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(derivation) Tj
100 Tz
1 0 0 1 340 291 Tm
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(and) Tj
100 Tz
1 0 0 1 362 291 Tm
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(implementation) Tj
100 Tz
1 0 0 1 436 291 Tm
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(of) Tj
100 Tz
1 0 0 1 451 291 Tm
(the) Tj
1 0 0 1 470 291 Tm
107 Tz
(equations) Tj
100 Tz
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(the) Tj
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(latter) Tj
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1 0 0 1 131 279 Tm
83 Tz
(is) Tj
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(preferable.) Tj
100 Tz
1 0 0 1 129 264 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 152 264 Tm
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(time) Tj
100 Tz
1 0 0 1 176 264 Tm
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(discretization) Tj
100 Tz
1 0 0 1 239 264 Tm
(is) Tj
1 0 0 1 250 264 Tm
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(parameterized) Tj
100 Tz
1 0 0 1 317 264 Tm
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(by) Tj
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1 0 0 1 331 264 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 341 264 Tm
109 Tz
(number) Tj
100 Tz
1 0 0 1 380 264 Tm
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(0) Tj
100 Tz
1 0 0 1 389 264 Tm
103 Tz
(obeying) Tj
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(0) Tj
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157 Tz
(\() Tj
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(0) Tj
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(I.) Tj
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100 Tz
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(=) Tj
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(this) Tj
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(gives) Tj
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(the) Tj
1 0 0 1 171 248 Tm
(very) Tj
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(stable) Tj
100 Tz
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(backward-Euler) Tj
100 Tz
1 0 0 1 298 248 Tm
106 Tz
(scheme,) Tj
100 Tz
1 0 0 1 339 248 Tm
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(0) Tj
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(=) Tj
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/F10 6 Tf
1 0 0 1 359 248 Tm
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(\205) Tj
100 Tz
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(gives) Tj
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(the) Tj
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100 Tz
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(icholson) Tj
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(scheme) Tj
100 Tz
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(2) Tj
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(and) Tj
100 Tz
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100 Tz
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(gives) Tj
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(the) Tj
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(rather) Tj
100 Tz
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(unstable) Tj
100 Tz
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(forward-Euler) Tj
100 Tz
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(scheme.) Tj
100 Tz
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(The) Tj
100 Tz
1 0 0 1 419 231 Tm
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(description) Tj
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1 0 0 1 433 545 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 441 545 Tm
103 Tz
(canonical) Tj
100 Tz
1 0 0 1 486 545 Tm
105 Tz
(form) Tj
100 Tz
1 0 0 1 510 545 Tm
122 Tz
(suit) Tj
100 Tz
(-) Tj
1 0 0 1 103 532 Tm
(able) Tj
1 0 0 1 124 532 Tm
(for) Tj
1 0 0 1 141 532 Tm
(use) Tj
1 0 0 1 159 532 Tm
(in) Tj
1 0 0 1 170 532 Tm
107 Tz
(Galerkin\202s) Tj
100 Tz
1 0 0 1 220 532 Tm
106 Tz
(method.) Tj
100 Tz
1 0 0 1 262 532 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 283 532 Tm
104 Tz
(linear) Tj
100 Tz
1 0 0 1 311 532 Tm
(BC\202s) Tj
1 0 0 1 336 532 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 360 532 Tm
(the) Tj
1 0 0 1 377 532 Tm
105 Tz
(form,) Tj
100 Tz
1 0 0 1 405 532 Tm
(at) Tj
1 0 0 1 416 532 Tm
(x) Tj
/F5 5 Tf
1 0 0 1 426 532 Tm
167 Tz
(=) Tj
100 Tz
/F12 10 Tf
1 0 0 1 437 532 Tm
83 Tz
(L) Tj
100 Tz
/F9 10 Tf
1 0 0 1 448 532 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 467 532 Tm
(x) Tj
/F5 5 Tf
1 0 0 1 477 532 Tm
167 Tz
(=) Tj
100 Tz
/F10 10 Tf
1 0 0 1 135 515 Tm
109 Tz
(au) Tj
100 Tz
/F10 8 Tf
1 0 0 1 150 515 Tm
129 Tz
(+flux) Tj
100 Tz
/F5 5 Tf
1 0 0 1 179 515 Tm
167 Tz
(=) Tj
100 Tz
/F9 10 Tf
1 0 0 1 508 515 Tm
(\(9.3\)) Tj
/F1 10 Tf
1 0 0 1 103 497 Tm
78 Tz
(For) Tj
100 Tz
1 0 0 1 122 497 Tm
50 Tz
(a) Tj
100 Tz
1 0 0 1 129 497 Tm
67 Tz
(scalar) Tj
100 Tz
1 0 0 1 157 497 Tm
77 Tz
(equation) Tj
100 Tz
/F8 8 Tf
1 0 0 1 199 497 Tm
(\(nu) Tj
/F5 5 Tf
1 0 0 1 217 497 Tm
167 Tz
(=) Tj
100 Tz
/F9 10 Tf
1 0 0 1 229 497 Tm
114 Tz
(I\)) Tj
100 Tz
1 0 0 1 241 497 Tm
109 Tz
(these) Tj
100 Tz
1 0 0 1 267 497 Tm
95 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 292 497 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 315 497 Tm
(the) Tj
1 0 0 1 333 497 Tm
105 Tz
(form) Tj
100 Tz
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1 0 0 1 135 479 Tm
117 Tz
(aU) Tj
100 Tz
1 0 0 1 151 479 Tm
112 Tz
(+/3Ux) Tj
100 Tz
/F5 5 Tf
1 0 0 1 179 479 Tm
167 Tz
(=) Tj
100 Tz
/F7 10 Tf
1 0 0 1 190 479 Tm
83 Tz
(Y) Tj
100 Tz
/F9 10 Tf
1 0 0 1 103 462 Tm
104 Tz
(which,) Tj
100 Tz
1 0 0 1 135 462 Tm
107 Tz
(depending) Tj
100 Tz
1 0 0 1 184 462 Tm
(on) Tj
1 0 0 1 198 462 Tm
109 Tz
(whether) Tj
100 Tz
/F10 13 Tf
1 0 0 1 237 462 Tm
50 Tz
(/3) Tj
100 Tz
/F5 5 Tf
1 0 0 1 247 462 Tm
167 Tz
(=) Tj
100 Tz
/F9 10 Tf
1 0 0 1 257 462 Tm
80 Tz
(0) Tj
100 Tz
1 0 0 1 266 462 Tm
(or) Tj
1 0 0 1 279 462 Tm
(not,) Tj
1 0 0 1 300 462 Tm
94 Tz
(may) Tj
100 Tz
1 0 0 1 322 462 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 335 462 Tm
103 Tz
(written) Tj
100 Tz
1 0 0 1 369 462 Tm
88 Tz
(as) Tj
100 Tz
1 0 0 1 381 462 Tm
112 Tz
(either) Tj
100 Tz
/F8 7 Tf
1 0 0 1 136 443 Tm
155 Tz
(UYD) Tj
100 Tz
/F9 10 Tf
1 0 0 1 188 443 Tm
134 Tz
(\(/3=0\)) Tj
100 Tz
/F1 10 Tf
1 0 0 1 158 425 Tm
67 Tz
(or) Tj
100 Tz
1 0 0 1 509 425 Tm
63 Tz
(\(9.4\)) Tj
100 Tz
/F11 10 Tf
1 0 0 1 136 407 Tm
113 Tz
(U~=AU\261y,~yf) Tj
100 Tz
/F9 10 Tf
1 0 0 1 210 407 Tm
151 Tz
(\(/3!=0\),) Tj
100 Tz
1 0 0 1 103 386 Tm
104 Tz
(where) Tj
100 Tz
/F8 8 Tf
1 0 0 1 133 386 Tm
(YD) Tj
/F5 5 Tf
1 0 0 1 148 386 Tm
167 Tz
(=) Tj
100 Tz
/F6 4 Tf
1 0 0 1 159 386 Tm
142 Tz
(-~-~) Tj
100 Tz
/F12 10 Tf
1 0 0 1 177 386 Tm
(A) Tj
/F5 5 Tf
1 0 0 1 188 386 Tm
167 Tz
(=) Tj
100 Tz
/F6 4 Tf
1 0 0 1 200 386 Tm
133 Tz
(\205) Tj
100 Tz
/F11 13 Tf
1 0 0 1 209 386 Tm
50 Tz
(-s--) Tj
100 Tz
/F9 10 Tf
1 0 0 1 224 386 Tm
107 Tz
(and) Tj
100 Tz
/F8 8 Tf
1 0 0 1 244 386 Tm
(YM) Tj
/F5 5 Tf
1 0 0 1 261 386 Tm
167 Tz
(=) Tj
100 Tz
/F6 4 Tf
1 0 0 1 273 386 Tm
(~) Tj
/F9 10 Tf
1 0 0 1 293 386 Tm
71 Tz
(A) Tj
100 Tz
/F9 11 Tf
1 0 0 1 304 386 Tm
(generaliiation) Tj
1 0 0 1 369 386 Tm
(of) Tj
1 0 0 1 382 386 Tm
(this) Tj
1 0 0 1 402 386 Tm
93 Tz
(canonical) Tj
100 Tz
1 0 0 1 446 386 Tm
95 Tz
(form) Tj
100 Tz
1 0 0 1 471 386 Tm
(for) Tj
/F12 10 Tf
1 0 0 1 489 386 Tm
73 Tz
(n~) Tj
100 Tz
/F5 5 Tf
1 0 0 1 502 386 Tm
167 Tz
(=) Tj
100 Tz
/F9 10 Tf
1 0 0 1 514 386 Tm
33 Tz
(I) Tj
100 Tz
1 0 0 1 522 386 Tm
(to) Tj
/F7 8 Tf
1 0 0 1 161 379 Tm
120 Tz
(a) Tj
100 Tz
/F10 13 Tf
1 0 0 1 211 379 Tm
60 Tz
(/3) Tj
100 Tz
1 0 0 1 274 379 Tm
50 Tz
(/3) Tj
100 Tz
/F9 10 Tf
1 0 0 1 103 368 Tm
106 Tz
(systems) Tj
100 Tz
1 0 0 1 141 368 Tm
106 Tz
(with) Tj
100 Tz
/F11 9 Tf
1 0 0 1 164 368 Tm
(~u) Tj
/F9 11 Tf
1 0 0 1 178 368 Tm
114 Tz
(\>) Tj
100 Tz
/F9 10 Tf
1 0 0 1 191 368 Tm
33 Tz
(I) Tj
100 Tz
1 0 0 1 199 368 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 209 368 Tm
(now) Tj
1 0 0 1 231 368 Tm
107 Tz
(presented.) Tj
100 Tz
1 0 0 1 282 368 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 306 368 Tm
107 Tz
(reduction) Tj
100 Tz
1 0 0 1 350 368 Tm
108 Tz
(assumes) Tj
100 Tz
1 0 0 1 391 368 Tm
(that) Tj
1 0 0 1 411 368 Tm
(each) Tj
1 0 0 1 435 368 Tm
92 Tz
(BC) Tj
100 Tz
1 0 0 1 452 368 Tm
(is) Tj
1 0 0 1 462 368 Tm
(for) Tj
1 0 0 1 478 368 Tm
(the) Tj
1 0 0 1 496 368 Tm
106 Tz
(purpose) Tj
100 Tz
1 0 0 1 103 356 Tm
(of) Tj
1 0 0 1 115 356 Tm
108 Tz
(determining) Tj
100 Tz
1 0 0 1 171 356 Tm
107 Tz
(one) Tj
100 Tz
1 0 0 1 191 356 Tm
(of) Tj
1 0 0 1 203 356 Tm
112 Tz
(either) Tj
100 Tz
/F11 10 Tf
1 0 0 1 233 356 Tm
80 Tz
(u) Tj
100 Tz
/F9 10 Tf
1 0 0 1 242 356 Tm
(or) Tj
/F11 14 Tf
1 0 0 1 256 356 Tm
61 Tz
(u~,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 272 356 Tm
108 Tz
(but) Tj
100 Tz
1 0 0 1 290 356 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 308 356 Tm
(both.) Tj
1 0 0 1 337 356 Tm
107 Tz
(For) Tj
100 Tz
1 0 0 1 356 356 Tm
108 Tz
(example,) Tj
100 Tz
1 0 0 1 400 356 Tm
(the) Tj
1 0 0 1 417 356 Tm
90 Tz
(\203BC\202s\204) Tj
100 Tz
/F8 8 Tf
1 0 0 1 136 340 Tm
119 Tz
(U\(O\)+Ux\(O\)) Tj
100 Tz
/F9 10 Tf
1 0 0 1 195 340 Tm
133 Tz
(=0) Tj
100 Tz
/F8 8 Tf
1 0 0 1 136 324 Tm
121 Tz
(U\(O\)41x\(O\)) Tj
100 Tz
/F9 10 Tf
1 0 0 1 194 324 Tm
128 Tz
(=0,) Tj
100 Tz
1 0 0 1 103 307 Tm
104 Tz
(which) Tj
100 Tz
1 0 0 1 133 307 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 143 307 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 152 307 Tm
(sloppy) Tj
1 0 0 1 184 307 Tm
94 Tz
(way) Tj
100 Tz
1 0 0 1 205 307 Tm
(to) Tj
1 0 0 1 217 307 Tm
92 Tz
(say) Tj
100 Tz
/F1 10 Tf
1 0 0 1 235 307 Tm
75 Tz
(u\(O\)) Tj
100 Tz
/F5 5 Tf
1 0 0 1 259 307 Tm
167 Tz
(=) Tj
100 Tz
/F9 10 Tf
1 0 0 1 269 307 Tm
80 Tz
(0) Tj
100 Tz
/F5 5 Tf
1 0 0 1 278 307 Tm
167 Tz
(=) Tj
100 Tz
/F1 10 Tf
1 0 0 1 290 307 Tm
69 Tz
(u~\(0\),) Tj
100 Tz
/F9 10 Tf
1 0 0 1 320 307 Tm
107 Tz
(cannot) Tj
100 Tz
1 0 0 1 354 307 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 369 307 Tm
105 Tz
(dealt) Tj
100 Tz
1 0 0 1 393 307 Tm
88 Tz
(with) Tj
100 Tz
1 0 0 1 417 307 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 431 307 Tm
(the) Tj
1 0 0 1 448 307 Tm
108 Tz
(proposed) Tj
100 Tz
1 0 0 1 492 307 Tm
114 Tz
(generali) Tj
100 Tz
(-) Tj
1 0 0 1 103 295 Tm
107 Tz
(zation,) Tj
100 Tz
1 0 0 1 136 295 Tm
110 Tz
(even) Tj
100 Tz
1 0 0 1 160 295 Tm
107 Tz
(though) Tj
100 Tz
1 0 0 1 195 295 Tm
(it) Tj
1 0 0 1 204 295 Tm
(is) Tj
1 0 0 1 214 295 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 227 295 Tm
(the) Tj
1 0 0 1 244 295 Tm
105 Tz
(form) Tj
100 Tz
1 0 0 1 269 295 Tm
105 Tz
(\(9.3\).) Tj
100 Tz
/F9 10 Tf
1 0 0 1 128 279 Tm
(Let) Tj
/F8 8 Tf
1 0 0 1 147 279 Tm
117 Tz
(aD) Tj
100 Tz
/F9 10 Tf
1 0 0 1 165 279 Tm
107 Tz
(and) Tj
100 Tz
/F8 8 Tf
1 0 0 1 186 279 Tm
(VD) Tj
/F9 10 Tf
1 0 0 1 203 279 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 219 279 Tm
(the) Tj
1 0 0 1 239 279 Tm
105 Tz
(Dirichlet) Tj
100 Tz
1 0 0 1 283 279 Tm
(IiC\202s,) Tj
1 0 0 1 312 279 Tm
(that) Tj
1 0 0 1 334 279 Tm
89 Tz
(is,) Tj
100 Tz
1 0 0 1 350 279 Tm
105 Tz
(those) Tj
100 Tz
1 0 0 1 378 279 Tm
(rows) Tj
1 0 0 1 404 279 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 418 279 Tm
120 Tz
(a) Tj
100 Tz
1 0 0 1 430 279 Tm
107 Tz
(and) Tj
100 Tz
/F7 14 Tf
1 0 0 1 451 279 Tm
71 Tz
(v) Tj
100 Tz
/F9 10 Tf
1 0 0 1 463 279 Tm
104 Tz
(which) Tj
100 Tz
1 0 0 1 494 279 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 519 279 Tm
90 Tz
(all) Tj
100 Tz
/F9 9 Tf
1 0 0 1 103 267 Tm
91 Tz
(/3,,) Tj
100 Tz
/F5 5 Tf
1 0 0 1 118 267 Tm
167 Tz
(=) Tj
100 Tz
/F9 10 Tf
1 0 0 1 129 267 Tm
(0.) Tj
1 0 0 1 144 267 Tm
107 Tz
(Let) Tj
100 Tz
/F8 8 Tf
1 0 0 1 163 267 Tm
119 Tz
(aM,) Tj
100 Tz
/F12 7 Tf
1 0 0 1 184 267 Tm
(~M) Tj
/F9 10 Tf
1 0 0 1 203 267 Tm
107 Tz
(and) Tj
100 Tz
/F12 7 Tf
1 0 0 1 223 267 Tm
123 Tz
(VM) Tj
100 Tz
/F1 10 Tf
1 0 0 1 242 267 Tm
67 Tz
(be) Tj
100 Tz
1 0 0 1 256 267 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 273 267 Tm
85 Tz
(complementary) Tj
100 Tz
/F12 10 Tf
1 0 0 1 345 267 Tm
50 Tz
(,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 352 267 Tm
104 Tz
(mixed,) Tj
100 Tz
1 0 0 1 386 267 Tm
109 Tz
(equations,) Tj
100 Tz
1 0 0 1 435 267 Tm
(that) Tj
1 0 0 1 456 267 Tm
89 Tz
(is,) Tj
100 Tz
1 0 0 1 470 267 Tm
(those) Tj
1 0 0 1 497 267 Tm
(rows) Tj
1 0 0 1 521 267 Tm
(of) Tj
/F12 10 Tf
1 0 0 1 103 255 Tm
112 Tz
(a,) Tj
100 Tz
/F7 14 Tf
1 0 0 1 116 255 Tm
(~) Tj
/F9 10 Tf
1 0 0 1 126 255 Tm
107 Tz
(and) Tj
100 Tz
/F7 14 Tf
1 0 0 1 146 255 Tm
71 Tz
(v) Tj
100 Tz
/F9 10 Tf
1 0 0 1 155 255 Tm
(which) Tj
1 0 0 1 184 255 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 208 255 Tm
105 Tz
(some) Tj
100 Tz
/F6 4 Tf
1 0 0 1 234 255 Tm
140 Tz
(/3,~) Tj
100 Tz
/F10 10 Tf
1 0 0 1 251 255 Tm
200 Tz
(!=) Tj
100 Tz
1 0 0 1 263 255 Tm
86 Tz
(0.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 127 240 Tm
92 Tz
(Then) Tj
100 Tz
/F8 8 Tf
1 0 0 1 156 240 Tm
109 Tz
(aD) Tj
100 Tz
/F9 10 Tf
1 0 0 1 173 240 Tm
93 Tz
(will) Tj
100 Tz
1 0 0 1 193 240 Tm
(be) Tj
1 0 0 1 208 240 Tm
(an) Tj
/F8 8 Tf
1 0 0 1 224 240 Tm
(flDX) Tj
/F11 9 Tf
1 0 0 1 244 240 Tm
89 Tz
(flu) Tj
100 Tz
/F9 10 Tf
1 0 0 1 259 240 Tm
107 Tz
(matrix,) Tj
100 Tz
1 0 0 1 295 240 Tm
104 Tz
(where) Tj
100 Tz
1 0 0 1 328 240 Tm
33 Tz
(I) Tj
100 Tz
/F10 10 Tf
1 0 0 1 336 240 Tm
157 Tz
(\() Tj
100 Tz
/F8 8 Tf
1 0 0 1 349 240 Tm
(~D) Tj
1 0 0 1 364 240 Tm
(~) Tj
1 0 0 1 377 240 Tm
(n~.) Tj
/F1 10 Tf
1 0 0 1 398 240 Tm
89 Tz
(The) Tj
100 Tz
1 0 0 1 421 240 Tm
69 Tz
(Dirichlet) Tj
100 Tz
1 0 0 1 465 240 Tm
79 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 490 240 Tm
79 Tz
(have) Tj
100 Tz
1 0 0 1 516 240 Tm
67 Tz
(the) Tj
100 Tz
/F9 11 Tf
1 0 0 1 103 225 Tm
95 Tz
(form) Tj
100 Tz
/F11 10 Tf
1 0 0 1 135 210 Tm
106 Tz
(aDu) Tj
100 Tz
/F5 5 Tf
1 0 0 1 158 210 Tm
167 Tz
(=) Tj
100 Tz
/F8 8 Tf
1 0 0 1 168 210 Tm
113 Tz
(VD\206) Tj
100 Tz
/F9 10 Tf
1 0 0 1 103 192 Tm
(Let) Tj
/F8 8 Tf
1 0 0 1 122 192 Tm
78 Tz
(flu) Tj
100 Tz
/F9 10 Tf
1 0 0 1 139 192 Tm
(be) Tj
1 0 0 1 154 192 Tm
(the) Tj
1 0 0 1 171 192 Tm
109 Tz
(number) Tj
100 Tz
1 0 0 1 209 192 Tm
111 Tz
(of) Tj
100 Tz
/F11 10 Tf
1 0 0 1 223 192 Tm
70 Tz
(u) Tj
-5 Ts

(1) Tj
100 Tz
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1 0 0 1 236 192 Tm
-5 Ts
(which) Tj
1 0 0 1 266 192 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 290 192 Tm
94 Tz
(am) Tj
-5 Ts

(1) Tj
100 Tz
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1 0 0 1 311 192 Tm
-5 Ts
200 Tz
(!=) Tj
100 Tz
1 0 0 1 324 192 Tm
(0) Tj
1 0 0 1 333 192 Tm
(for) Tj
1 0 0 1 349 192 Tm
105 Tz
(some) Tj
100 Tz
/F11 10 Tf
1 0 0 1 377 192 Tm
80 Tz
(i.) Tj
100 Tz
/F9 11 Tf
1 0 0 1 390 192 Tm
(Then) Tj
1 0 0 1 417 192 Tm
92 Tz
(we) Tj
100 Tz
1 0 0 1 433 192 Tm
95 Tz
(must) Tj
100 Tz
1 0 0 1 458 192 Tm
95 Tz
(have) Tj
100 Tz
/F12 7 Tf
1 0 0 1 483 192 Tm
93 Tz
(\203luD) Tj
100 Tz
1 0 0 1 501 192 Tm
(~) Tj
/F9 10 Tf
1 0 0 1 103 178 Tm
(for) Tj
1 0 0 1 119 178 Tm
107 Tz
(otherwise) Tj
100 Tz
1 0 0 1 165 178 Tm
(the) Tj
1 0 0 1 182 178 Tm
105 Tz
(Dirichlet) Tj
100 Tz
/F9 11 Tf
1 0 0 1 224 178 Tm
91 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 248 178 Tm
82 Tz
(will) Tj
100 Tz
1 0 0 1 267 178 Tm
80 Tz
(be) Tj
100 Tz
1 0 0 1 280 178 Tm
(overdetermined.) Tj
/F9 10 Tf
1 0 0 1 127 163 Tm
(We) Tj
1 0 0 1 146 163 Tm
94 Tz
(may) Tj
100 Tz
1 0 0 1 167 163 Tm
104 Tz
(obtain) Tj
100 Tz
1 0 0 1 197 163 Tm
(a) Tj
1 0 0 1 205 163 Tm
(QR) Tj
1 0 0 1 224 163 Tm
106 Tz
(factorization) Tj
100 Tz
/F9 14 Tf
1 0 0 1 282 163 Tm
(\[551) Tj
/F9 10 Tf
1 0 0 1 303 163 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 316 163 Tm
(the) Tj
1 0 0 1 333 163 Tm
105 Tz
(form) Tj
100 Tz
/F10 10 Tf
1 0 0 1 134 144 Tm
110 Tz
(QaDP) Tj
100 Tz
/F5 5 Tf
1 0 0 1 168 144 Tm
167 Tz
(=) Tj
100 Tz
/F10 10 Tf
1 0 0 1 179 144 Tm
67 Tz
(\() Tj
100 Tz
/F9 10 Tf
1 0 0 1 187 144 Tm
(R) Tj
/F9 9 Tf
1 0 0 1 199 144 Tm
142 Tz
(IC\)) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 126 Tm
104 Tz
(where) Tj
100 Tz
/F6 4 Tf
1 0 0 1 133 126 Tm
157 Tz
(Q) Tj
100 Tz
/F9 10 Tf
1 0 0 1 147 126 Tm
(is) Tj
/F9 10 Tf
1 0 0 1 158 126 Tm
(an) Tj
/F8 8 Tf
1 0 0 1 174 126 Tm
110 Tz
(flDXflD) Tj
100 Tz
/F9 10 Tf
1 0 0 1 209 126 Tm
107 Tz
(orthogonal) Tj
100 Tz
1 0 0 1 262 126 Tm
107 Tz
(matrix,) Tj
100 Tz
1 0 0 1 298 126 Tm
(P) Tj
1 0 0 1 310 126 Tm
(is) Tj
1 0 0 1 321 126 Tm
75 Tz
(a) Tj
100 Tz
/F8 8 Tf
1 0 0 1 332 126 Tm
107 Tz
(ri~~) Tj
100 Tz
1 0 0 1 350 126 Tm
(r~) Tj
/F9 10 Tf
1 0 0 1 364 126 Tm
108 Tz
(permutation) Tj
100 Tz
1 0 0 1 423 126 Tm
107 Tz
(matrix,) Tj
100 Tz
1 0 0 1 460 126 Tm
(R) Tj
1 0 0 1 473 126 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 484 126 Tm
(an) Tj
/F8 7 Tf
1 0 0 1 500 126 Tm
121 Tz
(flDXflD) Tj
100 Tz
/F9 10 Tf
1 0 0 1 103 114 Tm
108 Tz
(upper) Tj
100 Tz
1 0 0 1 132 114 Tm
107 Tz
(triangular) Tj
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1 0 0 1 250 675 Tm
83 Tz
(form) Tj
100 Tz
/F12 9 Tf
1 0 0 1 140 657 Tm
116 Tz
(aMy) Tj
100 Tz
/F2 7 Tf
1 0 0 1 163 657 Tm
136 Tz
(+PMUx) Tj
100 Tz
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1 0 0 1 201 657 Tm
167 Tz
(=) Tj
100 Tz
/F11 10 Tf
1 0 0 1 212 657 Tm
92 Tz
(YM) Tj
100 Tz
/F9 10 Tf
1 0 0 1 108 639 Tm
104 Tz
(where) Tj
100 Tz
/F12 9 Tf
1 0 0 1 140 639 Tm
131 Tz
(a~) Tj
100 Tz
/F9 10 Tf
1 0 0 1 160 639 Tm
(and) Tj
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1 0 0 1 180 639 Tm
(~M) Tj
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1 0 0 1 201 639 Tm
67 Tz
(are) Tj
100 Tz
/F2 7 Tf
1 0 0 1 220 639 Tm
111 Tz
(flMX) Tj
100 Tz
/F10 10 Tf
1 0 0 1 241 639 Tm
80 Tz
(n,,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 256 639 Tm
105 Tz
(matrices,) Tj
100 Tz
1 0 0 1 301 639 Tm
88 Tz
(with) Tj
100 Tz
1 0 0 1 326 639 Tm
20 Tz
(1) Tj
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1 0 0 1 335 639 Tm
(~) Tj
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1 0 0 1 365 639 Tm
150 Tz
(\() Tj
100 Tz
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85 Tz
(ri,) Tj
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(1) Tj
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100 Tz
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89 Tz
(be) Tj
100 Tz
1 0 0 1 454 639 Tm
(the) Tj
1 0 0 1 473 639 Tm
109 Tz
(number) Tj
100 Tz
/F10 7 Tf
1 0 0 1 512 639 Tm
(\(If) Tj
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1 0 0 1 527 639 Tm
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(u) Tj
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100 Tz
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(which) Tj
100 Tz
1 0 0 1 138 625 Tm
105 Tz
(have) Tj
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118 Tz
(/3Mij) Tj
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1 0 0 1 184 625 Tm
200 Tz
(!=) Tj
100 Tz
1 0 0 1 197 625 Tm
80 Tz
(0) Tj
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1 0 0 1 206 625 Tm
(for) Tj
1 0 0 1 222 625 Tm
105 Tz
(some) Tj
100 Tz
/F11 10 Tf
1 0 0 1 249 625 Tm
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(i.) Tj
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/F9 10 Tf
1 0 0 1 261 625 Tm
109 Tz
(Then) Tj
100 Tz
1 0 0 1 288 625 Tm
91 Tz
(we) Tj
100 Tz
1 0 0 1 304 625 Tm
105 Tz
(must) Tj
100 Tz
1 0 0 1 329 625 Tm
105 Tz
(have) Tj
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1 0 0 1 354 625 Tm
87 Tz
(ri,,~,) Tj
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1 0 0 1 386 625 Tm
114 Tz
(nq.) Tj
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1 0 0 1 405 625 Tm
(for) Tj
1 0 0 1 421 625 Tm
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(otherwise) Tj
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(the) Tj
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(mixed) Tj
100 Tz
1 0 0 1 515 625 Tm
95 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 108 610 Tm
(would) Tj
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(be) Tj
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(overdetermined.) Tj
100 Tz
1 0 0 1 232 610 Tm
103 Tz
(Precisely) Tj
100 Tz
1 0 0 1 275 610 Tm
(as) Tj
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(in) Tj
1 0 0 1 300 610 Tm
(the) Tj
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97 Tz
(Dirichilet) Tj
100 Tz
1 0 0 1 360 610 Tm
105 Tz
(case,) Tj
100 Tz
1 0 0 1 386 610 Tm
91 Tz
(we) Tj
100 Tz
1 0 0 1 402 610 Tm
94 Tz
(may) Tj
100 Tz
1 0 0 1 423 610 Tm
104 Tz
(obtain) Tj
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75 Tz
(a) Tj
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1 0 0 1 462 610 Tm
(QR) Tj
1 0 0 1 481 610 Tm
104 Tz
(factorization) Tj
100 Tz
1 0 0 1 108 598 Tm
(of) Tj
1 0 0 1 121 598 Tm
(the) Tj
1 0 0 1 138 598 Tm
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(form) Tj
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117 Tz
(Q~M) Tj
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1 0 0 1 166 578 Tm
83 Tz
(P) Tj
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1 0 0 1 176 578 Tm
167 Tz
(=) Tj
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67 Tz
(\() Tj
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(I) Tj
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(C\).) Tj
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89 Tz
(be) Tj
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1 0 0 1 157 563 Tm
(the) Tj
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110 Tz
(elements) Tj
100 Tz
1 0 0 1 254 563 Tm
111 Tz
(of) Tj
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(u) Tj
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(and) Tj
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90 Tz
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(u) Tj
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(the) Tj
1 0 0 1 370 563 Tm
(rest) Tj
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(of) Tj
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(~t) Tj
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1 0 0 1 414 563 Tm
(u.) Tj
1 0 0 1 428 563 Tm
109 Tz
(Then) Tj
100 Tz
/F12 7 Tf
1 0 0 1 140 544 Tm
125 Tz
(U~x) Tj
100 Tz
/F9 10 Tf
1 0 0 1 172 544 Tm
129 Tz
(R\202) Tj
100 Tz
/F12 9 Tf
1 0 0 1 190 544 Tm
136 Tz
(QVMRIQaMURICU.~x) Tj
100 Tz
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1 0 0 1 514 544 Tm
(\(9.6) Tj
1 0 0 1 108 527 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 131 527 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 141 527 Tm
(the) Tj
1 0 0 1 158 527 Tm
103 Tz
(canonical) Tj
100 Tz
1 0 0 1 202 527 Tm
105 Tz
(form) Tj
100 Tz
1 0 0 1 227 527 Tm
(which) Tj
1 0 0 1 256 527 Tm
93 Tz
(will) Tj
100 Tz
1 0 0 1 275 527 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 288 527 Tm
108 Tz
(assumed) Tj
100 Tz
1 0 0 1 330 527 Tm
(for) Tj
1 0 0 1 346 527 Tm
(the) Tj
1 0 0 1 363 527 Tm
104 Tz
(mixed) Tj
100 Tz
1 0 0 1 394 527 Tm
96 Tz
(BC\202s.) Tj
100 Tz
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94 Tz
(The) Tj
100 Tz
1 0 0 1 153 511 Tm
92 Tz
(above) Tj
100 Tz
1 0 0 1 182 511 Tm
86 Tz
(BC) Tj
100 Tz
1 0 0 1 199 511 Tm
96 Tz
(forms.) Tj
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1 0 0 1 232 511 Tm
(\(9.5\)) Tj
1 0 0 1 256 511 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 277 511 Tm
109 Tz
(\(9.6\),) Tj
100 Tz
1 0 0 1 305 511 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 329 511 Tm
(the) Tj
1 0 0 1 346 511 Tm
105 Tz
(form) Tj
100 Tz
/F10 8 Tf
1 0 0 1 140 493 Tm
91 Tz
(UD) Tj
100 Tz
/F5 5 Tf
1 0 0 1 154 493 Tm
171 Tz
(=) Tj
100 Tz
/F12 9 Tf
1 0 0 1 165 493 Tm
112 Tz
(VD+CDU) Tj
100 Tz
/F9 10 Tf
1 0 0 1 514 475 Tm
116 Tz
(\(97\)) Tj
100 Tz
/F8 7 Tf
1 0 0 1 140 457 Tm
106 Tz
(UMX) Tj
100 Tz
/F5 5 Tf
1 0 0 1 161 457 Tm
167 Tz
(=) Tj
100 Tz
/F6 10 Tf
1 0 0 1 172 457 Tm
85 Tz
(Au) Tj
100 Tz
/F8 9 Tf
1 0 0 1 187 457 Tm
118 Tz
(+VM) Tj
100 Tz
/F9 10 Tf
1 0 0 1 212 457 Tm
105 Tz
(+CM) Tj
100 Tz
/F6 8 Tf
1 0 0 1 238 457 Tm
90 Tz
(uX) Tj
100 Tz
/F9 10 Tf
1 0 0 1 108 439 Tm
104 Tz
(where) Tj
100 Tz
1 0 0 1 137 439 Tm
(the) Tj
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106 Tz
(appropriate) Tj
100 Tz
1 0 0 1 207 439 Tm
111 Tz
(columns) Tj
100 Tz
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(of) Tj
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(CD,) Tj
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82 Tz
(CM) Tj
100 Tz
1 0 0 1 297 439 Tm
(and) Tj
1 0 0 1 317 439 Tm
86 Tz
(A) Tj
100 Tz
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92 Tz
(are) Tj
100 Tz
1 0 0 1 344 439 Tm
95 Tz
(zero.) Tj
100 Tz
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106 Tz
(The) Tj
100 Tz
1 0 0 1 154 424 Tm
108 Tz
(above) Tj
100 Tz
1 0 0 1 184 424 Tm
105 Tz
(form) Tj
100 Tz
/F9 10 Tf
1 0 0 1 210 424 Tm
105 Tz
(\(9.7\)) Tj
100 Tz
1 0 0 1 236 424 Tm
106 Tz
(generalizes) Tj
100 Tz
1 0 0 1 289 424 Tm
(the) Tj
1 0 0 1 307 424 Tm
108 Tz
(standard) Tj
100 Tz
1 0 0 1 349 424 Tm
105 Tz
(form) Tj
100 Tz
1 0 0 1 375 424 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 392 424 Tm
104 Tz
(linear) Tj
100 Tz
1 0 0 1 421 424 Tm
(BC\202s) Tj
1 0 0 1 446 424 Tm
105 Tz
(when) Tj
100 Tz
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67 Tz
(re,,) Tj
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167 Tz
(=) Tj
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33 Tz
(I) Tj
100 Tz
1 0 0 1 508 424 Tm
(to) Tj
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(case) Tj
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104 Tz
(where) Tj
100 Tz
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(~) Tj
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129 Tz
(\>) Tj
100 Tz
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71 Tz
(1.) Tj
100 Tz
1 0 0 1 201 411 Tm
83 Tz
(It) Tj
100 Tz
1 0 0 1 211 411 Tm
94 Tz
(may) Tj
100 Tz
1 0 0 1 233 411 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 251 411 Tm
110 Tz
(represent) Tj
100 Tz
1 0 0 1 296 411 Tm
(the) Tj
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(most) Tj
100 Tz
1 0 0 1 338 411 Tm
103 Tz
(general) Tj
100 Tz
1 0 0 1 373 411 Tm
106 Tz
(generalization,) Tj
100 Tz
1 0 0 1 442 411 Tm
108 Tz
(but) Tj
100 Tz
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(it) Tj
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83 Tz
(is) Tj
100 Tz
1 0 0 1 479 411 Tm
105 Tz
(sufficient) Tj
100 Tz
1 0 0 1 522 411 Tm
65 Tz
(f~or) Tj
100 Tz
/F1 10 Tf
1 0 0 1 107 400 Tm
50 Tz
(all) Tj
100 Tz
1 0 0 1 121 400 Tm
81 Tz
(problems) Tj
100 Tz
/F9 10 Tf
1 0 0 1 165 400 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 177 400 Tm
(which) Tj
1 0 0 1 207 400 Tm
(the) Tj
1 0 0 1 224 400 Tm
107 Tz
(author) Tj
100 Tz
1 0 0 1 256 400 Tm
(is) Tj
1 0 0 1 266 400 Tm
104 Tz
(aware,) Tj
100 Tz
1 0 0 1 297 400 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 317 400 Tm
106 Tz
(then) Tj
100 Tz
1 0 0 1 340 400 Tm
104 Tz
(some.) Tj
100 Tz
/F10 10 Tf
1 0 0 1 108 376 Tm
92 Tz
(BC) Tj
100 Tz
1 0 0 1 125 376 Tm
106 Tz
(Placement.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 132 360 Tm
107 Tz
(Galerkin\202s) Tj
100 Tz
1 0 0 1 182 360 Tm
106 Tz
(method) Tj
100 Tz
1 0 0 1 220 360 Tm
106 Tz
(reduces) Tj
100 Tz
1 0 0 1 258 360 Tm
113 Tz
(\(9.l\)-\(9.2\)) Tj
100 Tz
1 0 0 1 309 360 Tm
(to) Tj
1 0 0 1 322 360 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 330 360 Tm
107 Tz
(system) Tj
100 Tz
1 0 0 1 364 360 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 378 360 Tm
104 Tz
(linear) Tj
100 Tz
1 0 0 1 406 360 Tm
103 Tz
(algebraic) Tj
100 Tz
1 0 0 1 448 360 Tm
107 Tz
(equations) Tj
100 Tz
1 0 0 1 495 360 Tm
(in) Tj
1 0 0 1 508 360 Tm
(the) Tj
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125 Tz
(B) Tj
100 Tz
(-) Tj
1 0 0 1 107 348 Tm
92 Tz
(sphine) Tj
100 Tz
1 0 0 1 137 348 Tm
104 Tz
(coefficients) Tj
100 Tz
1 0 0 1 190 348 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 207 348 Tm
(the) Tj
1 0 0 1 224 348 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 263 348 Tm
112 Tz
(u,) Tj
100 Tz
1 0 0 1 276 348 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 291 348 Tm
(making) Tj
1 0 0 1 327 348 Tm
(the) Tj
1 0 0 1 344 348 Tm
110 Tz
(error) Tj
100 Tz
1 0 0 1 370 348 Tm
(in) Tj
1 0 0 1 383 348 Tm
(\(9.) Tj
1 0 0 1 396 348 Tm
75 Tz
(1\)) Tj
100 Tz
1 0 0 1 408 348 Tm
107 Tz
(orthogonal) Tj
100 Tz
1 0 0 1 459 348 Tm
(to) Tj
1 0 0 1 471 348 Tm
89 Tz
(each) Tj
100 Tz
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111 Tz
(of) Tj
100 Tz
1 0 0 1 508 348 Tm
(the) Tj
1 0 0 1 525 348 Tm
125 Tz
(B) Tj
100 Tz
(-) Tj
1 0 0 1 107 336 Tm
92 Tz
(sphine) Tj
100 Tz
1 0 0 1 140 336 Tm
(basis) Tj
1 0 0 1 167 336 Tm
105 Tz
(functions) Tj
100 Tz
/F10 6 Tf
1 0 0 1 214 336 Tm
(\[421.) Tj
/F9 10 Tf
1 0 0 1 243 336 Tm
106 Tz
(Certain) Tj
100 Tz
1 0 0 1 282 336 Tm
(of) Tj
1 0 0 1 298 336 Tm
105 Tz
(these) Tj
100 Tz
1 0 0 1 326 336 Tm
102 Tz
(orthogonahity) Tj
100 Tz
1 0 0 1 391 336 Tm
106 Tz
(relations) Tj
100 Tz
1 0 0 1 435 336 Tm
(are) Tj
1 0 0 1 455 336 Tm
106 Tz
(then) Tj
100 Tz
1 0 0 1 480 336 Tm
103 Tz
(replaced,) Tj
100 Tz
1 0 0 1 525 336 Tm
(or) Tj
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1 0 0 1 108 324 Tm
105 Tz
(modified,) Tj
100 Tz
1 0 0 1 153 324 Tm
90 Tz
(by) Tj
100 Tz
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1 0 0 1 167 324 Tm
85 Tz
(BC) Tj
100 Tz
1 0 0 1 184 324 Tm
107 Tz
(equations.) Tj
100 Tz
1 0 0 1 236 324 Tm
86 Tz
(A) Tj
100 Tz
1 0 0 1 247 324 Tm
92 Tz
(BC) Tj
100 Tz
1 0 0 1 264 324 Tm
(on) Tj
/F11 10 Tf
1 0 0 1 280 324 Tm
86 Tz
(u,) Tj
100 Tz
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1 0 0 1 291 324 Tm
(at) Tj
1 0 0 1 303 324 Tm
(x) Tj
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1 0 0 1 313 324 Tm
167 Tz
(=) Tj
100 Tz
/F12 10 Tf
1 0 0 1 324 324 Tm
83 Tz
(L) Tj
100 Tz
/F9 10 Tf
1 0 0 1 335 324 Tm
104 Tz
(affects) Tj
100 Tz
1 0 0 1 368 324 Tm
(the) Tj
1 0 0 1 385 324 Tm
(first) Tj
1 0 0 1 405 324 Tm
107 Tz
(orthogonality) Tj
100 Tz
1 0 0 1 468 324 Tm
106 Tz
(relation) Tj
100 Tz
1 0 0 1 505 324 Tm
(for) Tj
1 0 0 1 521 324 Tm
(the) Tj
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1 0 0 1 108 312 Tm
112 Tz
(ith) Tj
100 Tz
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1 0 0 1 123 312 Tm
104 Tz
(ODE.) Tj
100 Tz
1 0 0 1 157 312 Tm
102 Tz
(Similarly,) Tj
100 Tz
1 0 0 1 203 312 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 213 312 Tm
92 Tz
(BC) Tj
100 Tz
1 0 0 1 231 312 Tm
(on) Tj
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1 0 0 1 248 312 Tm
80 Tz
(u) Tj
100 Tz
/F9 10 Tf
1 0 0 1 260 312 Tm
(at) Tj
1 0 0 1 273 312 Tm
(x) Tj
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1 0 0 1 283 312 Tm
167 Tz
(=) Tj
100 Tz
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1 0 0 1 294 312 Tm
(R) Tj
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1 0 0 1 308 312 Tm
93 Tz
(afTects) Tj
100 Tz
1 0 0 1 341 312 Tm
(the) Tj
1 0 0 1 359 312 Tm
(last,) Tj
/F1 10 Tf
1 0 0 1 382 312 Tm
86 Tz
(N~kst,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 420 312 Tm
106 Tz
(relation) Tj
100 Tz
1 0 0 1 458 312 Tm
(for) Tj
1 0 0 1 476 312 Tm
(the) Tj
/F1 10 Tf
1 0 0 1 495 312 Tm
44 Tz
(i\204\202) Tj
100 Tz
/F1 10 Tf
1 0 0 1 509 312 Tm
70 Tz
(Oli~E) Tj
100 Tz
/F9 10 Tf
1 0 0 1 107 300 Tm
107 Tz
(Galerkin\202s) Tj
100 Tz
1 0 0 1 158 300 Tm
106 Tz
(method) Tj
100 Tz
1 0 0 1 196 300 Tm
106 Tz
(requires) Tj
100 Tz
1 0 0 1 237 300 Tm
(that) Tj
1 0 0 1 258 300 Tm
107 Tz
(certain) Tj
100 Tz
1 0 0 1 293 300 Tm
95 Tz
(BC\202s) Tj
100 Tz
1 0 0 1 318 300 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 333 300 Tm
102 Tz
(associated) Tj
100 Tz
1 0 0 1 382 300 Tm
(with) Tj
1 0 0 1 406 300 Tm
103 Tz
(\(applied) Tj
100 Tz
1 0 0 1 446 300 Tm
(to\)) Tj
1 0 0 1 463 300 Tm
104 Tz
(certain) Tj
100 Tz
1 0 0 1 498 300 Tm
105 Tz
(kinds) Tj
100 Tz
1 0 0 1 525 300 Tm
88 Tz
(of) Tj
100 Tz
1 0 0 1 107 288 Tm
106 Tz
(differential) Tj
100 Tz
1 0 0 1 161 288 Tm
107 Tz
(equations.) Tj
100 Tz
1 0 0 1 215 288 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 239 288 Tm
106 Tz
(restrictions) Tj
100 Tz
1 0 0 1 294 288 Tm
107 Tz
(\(assumptions\)) Tj
100 Tz
1 0 0 1 362 288 Tm
105 Tz
(made) Tj
100 Tz
1 0 0 1 392 288 Tm
(upon) Tj
1 0 0 1 420 288 Tm
(the) Tj
1 0 0 1 440 288 Tm
106 Tz
(relation) Tj
100 Tz
1 0 0 1 479 288 Tm
106 Tz
(between) Tj
100 Tz
1 0 0 1 521 288 Tm
(the) Tj
1 0 0 1 107 276 Tm
111 Tz
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1 0 0 1 384 528 Tm
107 Tz
(presented) Tj
100 Tz
1 0 0 1 430 528 Tm
(at) Tj
1 0 0 1 443 528 Tm
(the) Tj
1 0 0 1 460 528 Tm
(SIAM) Tj
1 0 0 1 491 528 Tm
106 Tz
(National) Tj
100 Tz
/F1 10 Tf
1 0 0 1 127 515 Tm
77 Tz
(Meeting,) Tj
100 Tz
1 0 0 1 170 515 Tm
82 Tz
(Washington,) Tj
100 Tz
1 0 0 1 229 515 Tm
83 Tz
(June) Tj
100 Tz
1 0 0 1 256 515 Tm
70 Tz
(1971,) Tj
100 Tz
1 0 0 1 283 515 Tm
78 Tz
(and) Tj
100 Tz
/F9 10 Tf
1 0 0 1 303 515 Tm
(at) Tj
1 0 0 1 316 515 Tm
(the) Tj
1 0 0 1 333 515 Tm
108 Tz
(Coqference) Tj
100 Tz
1 0 0 1 389 515 Tm
(on) Tj
1 0 0 1 404 515 Tm
103 Tz
(Ordinary) Tj
100 Tz
1 0 0 1 447 515 Tm
106 Tz
(Differential) Tj
100 Tz
1 0 0 1 502 515 Tm
117 Tz
(Equa) Tj
100 Tz
(-) Tj
/F9 10 Tf
1 0 0 1 127 504 Tm
105 Tz
(tions,) Tj
100 Tz
1 0 0 1 154 504 Tm
108 Tz
(Dundee,) Tj
100 Tz
1 0 0 1 195 504 Tm
105 Tz
(Scotland,) Tj
100 Tz
1 0 0 1 239 504 Tm
106 Tz
(August,) Tj
100 Tz
1 0 0 1 278 504 Tm
95 Tz
(1971.) Tj
100 Tz
1 0 0 1 102 489 Tm
(\[291) Tj
1 0 0 1 126 489 Tm
105 Tz
(A.D.) Tj
100 Tz
1 0 0 1 151 489 Tm
94 Tz
(Hall) Tj
100 Tz
1 0 0 1 172 489 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 191 489 Tm
115 Tz
(SI.) Tj
100 Tz
1 0 0 1 209 489 Tm
107 Tz
(Feldman,) Tj
100 Tz
1 0 0 1 254 489 Tm
(\203EFL,) Tj
1 0 0 1 284 489 Tm
(an) Tj
1 0 0 1 298 489 Tm
107 Tz
(Extended) Tj
100 Tz
1 0 0 1 343 489 Tm
106 Tz
(FORTRAN) Tj
100 Tz
1 0 0 1 397 489 Tm
(Language\204,) Tj
1 0 0 1 450 489 Tm
(in) Tj
1 0 0 1 461 489 Tm
104 Tz
(preparation.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 473 Tm
(\[301) Tj
/F9 10 Tf
1 0 0 1 126 473 Tm
118 Tz
(TE.) Tj
100 Tz
1 0 0 1 148 473 Tm
(Hull,) Tj
1 0 0 1 173 473 Tm
123 Tz
(Wil.) Tj
100 Tz
1 0 0 1 201 473 Tm
106 Tz
(Enright,) Tj
100 Tz
1 0 0 1 240 473 Tm
(B.M.) Tj
1 0 0 1 265 473 Tm
(Fellen) Tj
1 0 0 1 295 473 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 314 473 Tm
111 Tz
(AU.) Tj
100 Tz
1 0 0 1 337 473 Tm
102 Tz
(Sedgwick,) Tj
100 Tz
1 0 0 1 385 473 Tm
104 Tz
(\203Comparing) Tj
100 Tz
1 0 0 1 441 473 Tm
105 Tz
(Numerical) Tj
100 Tz
1 0 0 1 490 473 Tm
105 Tz
(Methods) Tj
100 Tz
/F9 10 Tf
1 0 0 1 126 461 Tm
(for) Tj
1 0 0 1 142 461 Tm
103 Tz
(Ordinary) Tj
100 Tz
1 0 0 1 184 461 Tm
106 Tz
(Differential) Tj
100 Tz
1 0 0 1 238 461 Tm
104 Tz
(Equations\204,) Tj
100 Tz
1 0 0 1 291 461 Tm
105 Tz
(Technical) Tj
100 Tz
1 0 0 1 337 461 Tm
104 Tz
(Report) Tj
100 Tz
1 0 0 1 370 461 Tm
(29,) Tj
/F9 10 Tf
1 0 0 1 388 461 Tm
(1971,) Tj
1 0 0 1 415 461 Tm
108 Tz
(Department) Tj
100 Tz
1 0 0 1 471 461 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 483 461 Tm
107 Tz
(Computer) Tj
100 Tz
/F9 10 Tf
1 0 0 1 126 449 Tm
103 Tz
(Sciences,) Tj
100 Tz
1 0 0 1 169 449 Tm
102 Tz
(University) Tj
100 Tz
1 0 0 1 218 449 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 230 449 Tm
108 Tz
(Toronto.) Tj
100 Tz
/F10 7 Tf
1 0 0 1 102 433 Tm
(\[311) Tj
1 0 0 1 126 433 Tm
112 Tz
(H.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 144 433 Tm
(Ikezi,) Tj
/F9 10 Tf
1 0 0 1 175 433 Tm
117 Tz
(AL.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 202 433 Tm
106 Tz
(Simons,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 244 433 Tm
106 Tz
(K.F.) Tj
100 Tz
1 0 0 1 271 433 Tm
104 Tz
(Schwarzenegger) Tj
100 Tz
1 0 0 1 348 433 Tm
(and) Tj
1 0 0 1 371 433 Tm
(T.S.) Tj
1 0 0 1 396 433 Tm
106 Tz
(Kamimura,) Tj
100 Tz
1 0 0 1 453 433 Tm
104 Tz
(\203Nonlinear) Tj
100 Tz
1 0 0 1 507 433 Tm
(Self-) Tj
/F9 10 Tf
1 0 0 1 126 422 Tm
106 Tz
(Modulation) Tj
100 Tz
1 0 0 1 180 422 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 192 422 Tm
107 Tz
(lon-Accoustic) Tj
100 Tz
1 0 0 1 256 422 Tm
104 Tz
(Wave) Tj
100 Tz
1 0 0 1 285 422 Tm
(Packets\204,) Tj
1 0 0 1 328 422 Tm
(to) Tj
1 0 0 1 340 422 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 353 422 Tm
109 Tz
(submitted) Tj
100 Tz
1 0 0 1 401 422 Tm
(to) Tj
/F11 10 Tf
1 0 0 1 413 422 Tm
(Physics) Tj
1 0 0 1 446 422 Tm
122 Tz
(of) Tj
100 Tz
1 0 0 1 457 422 Tm
93 Tz
(Fluids.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 406 Tm
(\[321) Tj
1 0 0 1 126 406 Tm
95 Tz
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100 Tz
1 0 0 1 153 406 Tm
106 Tz
(Kernighan,) Tj
100 Tz
1 0 0 1 207 406 Tm
104 Tz
(\203RATFOR) Tj
100 Tz
/F10 4 Tf
1 0 0 1 258 406 Tm
150 Tz
(-) Tj
100 Tz
/F9 10 Tf
1 0 0 1 268 406 Tm
71 Tz
(A) Tj
100 Tz
1 0 0 1 280 406 Tm
107 Tz
(Preprocessor) Tj
100 Tz
1 0 0 1 341 406 Tm
(for) Tj
1 0 0 1 359 406 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 369 406 Tm
106 Tz
(Rational) Tj
100 Tz
1 0 0 1 410 406 Tm
105 Tz
(Fortran\204,) Tj
100 Tz
/F3 10 Tf
1 0 0 1 455 406 Tm
71 Tz
(Software-Practice) Tj
100 Tz
/F11 10 Tf
1 0 0 1 126 394 Tm
94 Tz
(arid) Tj
100 Tz
1 0 0 1 145 394 Tm
96 Tz
(Experierice) Tj
100 Tz
/F1 10 Tf
1 0 0 1 192 394 Tm
58 Tz
(5,) Tj
100 Tz
1 0 0 1 204 394 Tm
79 Tz
(395-406\(1975\).) Tj
100 Tz
/F9 14 Tf
1 0 0 1 102 379 Tm
(\[331) Tj
/F1 10 Tf
1 0 0 1 125 379 Tm
50 Tz
(J.) Tj
100 Tz
1 0 0 1 142 379 Tm
98 Tz
(MeKenna) Tj
100 Tz
/F1 10 Tf
1 0 0 1 192 379 Tm
78 Tz
(and) Tj
100 Tz
1 0 0 1 216 379 Tm
75 Tz
(N.L.) Tj
100 Tz
1 0 0 1 245 379 Tm
73 Tz
(Schryer,) Tj
100 Tz
1 0 0 1 290 379 Tm
74 Tz
(\203Analysis) Tj
100 Tz
/F9 10 Tf
1 0 0 1 339 379 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 356 379 Tm
106 Tz
(Eield-Aided) Tj
100 Tz
1 0 0 1 416 379 Tm
107 Tz
(Charge-Coupled) Tj
100 Tz
1 0 0 1 497 379 Tm
103 Tz
(Device) Tj
100 Tz
/F9 10 Tf
1 0 0 1 125 367 Tm
105 Tz
(Transfer\204,) Tj
100 Tz
/F12 10 Tf
1 0 0 1 173 367 Tm
(BSTJ) Tj
/F10 10 Tf
1 0 0 1 199 367 Tm
(54,) Tj
/F9 10 Tf
1 0 0 1 216 367 Tm
107 Tz
(667-685\(1975\).) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 351 Tm
(\[341) Tj
/F9 10 Tf
1 0 0 1 126 351 Tm
(P.M.) Tj
1 0 0 1 153 351 Tm
104 Tz
(Morse) Tj
100 Tz
1 0 0 1 186 351 Tm
(and) Tj
1 0 0 1 208 351 Tm
89 Tz
(H.) Tj
100 Tz
1 0 0 1 224 351 Tm
107 Tz
(Feshbach,) Tj
100 Tz
1 0 0 1 275 351 Tm
105 Tz
(Methods) Tj
100 Tz
/F10 10 Tf
1 0 0 1 319 351 Tm
(of) Tj
1 0 0 1 333 351 Tm
104 Tz
(Theoretical) Tj
100 Tz
/F1 10 Tf
1 0 0 1 391 351 Tm
75 Tz
(Physics,) Tj
100 Tz
1 0 0 1 435 351 Tm
(Mc) Tj
1 0 0 1 454 351 Tm
75 Tz
(Graw-Hill,) Tj
100 Tz
1 0 0 1 507 351 Tm
(New) Tj
1 0 0 1 126 339 Tm
77 Tz
(York,) Tj
100 Tz
1 0 0 1 155 339 Tm
70 Tz
(1953.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 323 Tm
(\[351) Tj
/F9 10 Tf
1 0 0 1 126 323 Tm
116 Tz
(RD.) Tj
100 Tz
1 0 0 1 152 323 Tm
106 Tz
(Richtmeyer) Tj
100 Tz
1 0 0 1 208 323 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 230 323 Tm
(K.W.) Tj
1 0 0 1 259 323 Tm
109 Tz
(Morton,) Tj
100 Tz
/F10 10 Tf
1 0 0 1 301 323 Tm
(Difference) Tj
1 0 0 1 352 323 Tm
103 Tz
(Methods) Tj
100 Tz
1 0 0 1 397 323 Tm
(for) Tj
1 0 0 1 415 323 Tm
104 Tz
(Initial) Tj
100 Tz
1 0 0 1 449 323 Tm
(Value) Tj
1 0 0 1 482 323 Tm
(Problems,) Tj
/F9 10 Tf
1 0 0 1 126 312 Tm
107 Tz
(lnterscience,) Tj
100 Tz
1 0 0 1 185 312 Tm
(New) Tj
1 0 0 1 208 312 Tm
(York,) Tj
1 0 0 1 237 312 Tm
95 Tz
(1967.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 102 297 Tm
(\[361) Tj
1 0 0 1 126 297 Tm
75 Tz
(B.G.) Tj
100 Tz
1 0 0 1 151 297 Tm
83 Tz
(Ryder) Tj
100 Tz
1 0 0 1 182 297 Tm
78 Tz
(and) Tj
100 Tz
1 0 0 1 202 297 Tm
110 Tz
(AD.) Tj
100 Tz
1 0 0 1 229 297 Tm
53 Tz
(l\]aIl,) Tj
100 Tz
1 0 0 1 255 297 Tm
83 Tz
(\203The) Tj
100 Tz
1 0 0 1 281 297 Tm
106 Tz
(PEORT) Tj
100 Tz
1 0 0 1 319 297 Tm
65 Tz
(Verifier\204.) Tj
100 Tz
1 0 0 1 364 297 Tm
63 Tz
(Bell) Tj
100 Tz
1 0 0 1 386 297 Tm
75 Tz
(Laboratories) Tj
100 Tz
1 0 0 1 445 297 Tm
92 Tz
(Computer) Tj
100 Tz
/F9 10 Tf
1 0 0 1 494 297 Tm
(Science) Tj
/F9 10 Tf
1 0 0 1 125 285 Tm
105 Tz
(Technical) Tj
100 Tz
1 0 0 1 171 285 Tm
104 Tz
(Report) Tj
100 Tz
1 0 0 1 204 285 Tm
115 Tz
(#12,) Tj
100 Tz
1 0 0 1 230 285 Tm
95 Tz
(1975.) Tj
100 Tz
/F9 14 Tf
1 0 0 1 102 273 Tm
(\[371) Tj
/F9 10 Tf
1 0 0 1 126 273 Tm
111 Tz
(RA.) Tj
100 Tz
1 0 0 1 151 273 Tm
95 Tz
(Sack) Tj
100 Tz
1 0 0 1 176 273 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 197 273 Tm
106 Tz
(A.F) Tj
100 Tz
1 0 0 1 220 273 Tm
107 Tz
(Donovan,) Tj
100 Tz
1 0 0 1 268 273 Tm
(\203An) Tj
1 0 0 1 291 273 Tm
107 Tz
(Algorithm) Tj
100 Tz
1 0 0 1 341 273 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 359 273 Tm
108 Tz
(Gaussian) Tj
100 Tz
1 0 0 1 404 273 Tm
108 Tz
(Quadrature) Tj
100 Tz
1 0 0 1 458 273 Tm
104 Tz
(given) Tj
100 Tz
1 0 0 1 488 273 Tm
(Modified) Tj
/F9 10 Tf
1 0 0 1 126 257 Tm
104 Tz
(Moments\204,) Tj
100 Tz
/F11 10 Tf
1 0 0 1 177 257 Tm
94 Tz
(NUmer.) Tj
100 Tz
1 0 0 1 212 257 Tm
104 Tz
(Math.) Tj
100 Tz
/F10 10 Tf
1 0 0 1 244 257 Tm
(18,) Tj
/F1 10 Tf
1 0 0 1 261 257 Tm
80 Tz
(465-478\(1972\).) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 242 Tm
(\[381) Tj
1 0 0 1 126 242 Tm
112 Tz
(lW.) Tj
100 Tz
1 0 0 1 149 242 Tm
105 Tz
(Sandberg) Tj
100 Tz
1 0 0 1 195 242 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 216 242 Tm
89 Tz
(H.) Tj
100 Tz
1 0 0 1 231 242 Tm
107 Tz
(Shichman,) Tj
100 Tz
1 0 0 1 283 242 Tm
104 Tz
(\203Numerical) Tj
100 Tz
1 0 0 1 338 242 Tm
109 Tz
(Integration) Tj
100 Tz
1 0 0 1 391 242 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 405 242 Tm
103 Tz
(Systems) Tj
100 Tz
1 0 0 1 446 242 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 460 242 Tm
90 Tz
(StifT) Tj
100 Tz
1 0 0 1 483 242 Tm
107 Tz
(Nonlinear) Tj
100 Tz
/F9 10 Tf
1 0 0 1 126 231 Tm
104 Tz
(Differential) Tj
100 Tz
1 0 0 1 179 231 Tm
104 Tz
(Equations\204,) Tj
100 Tz
/F12 10 Tf
1 0 0 1 233 231 Tm
96 Tz
(BSTJ) Tj
100 Tz
1 0 0 1 258 231 Tm
(47,) Tj
/F1 10 Tf
1 0 0 1 276 231 Tm
79 Tz
(511-528\(1968\).) Tj
100 Tz
/F9 14 Tf
1 0 0 1 102 214 Tm
(\[391) Tj
/F9 10 Tf
1 0 0 1 126 214 Tm
(N.L.) Tj
1 0 0 1 149 214 Tm
103 Tz
(Schryer) Tj
100 Tz
1 0 0 1 186 214 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 207 214 Tm
(L.R.) Tj
1 0 0 1 230 214 Tm
106 Tz
(Walker,) Tj
100 Tz
1 0 0 1 269 214 Tm
105 Tz
(\203The) Tj
100 Tz
1 0 0 1 294 214 Tm
103 Tz
(Motion) Tj
100 Tz
1 0 0 1 330 214 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 345 214 Tm
85 Tz
(1800) Tj
100 Tz
1 0 0 1 369 214 Tm
103 Tz
(Domain) Tj
100 Tz
/F9 10 Tf
1 0 0 1 408 214 Tm
(Walls) Tj
1 0 0 1 436 214 Tm
(in) Tj
1 0 0 1 449 214 Tm
106 Tz
(Uniform) Tj
100 Tz
1 0 0 1 490 214 Tm
89 Tz
(dc) Tj
100 Tz
1 0 0 1 504 214 Tm
114 Tz
(Mag) Tj
100 Tz
(-) Tj
1 0 0 1 126 203 Tm
(netic) Tj
/F1 10 Tf
1 0 0 1 150 203 Tm
65 Tz
(Fields\204,) Tj
100 Tz
/F12 10 Tf
1 0 0 1 186 203 Tm
(I.) Tj
/F11 10 Tf
1 0 0 1 197 203 Tm
95 Tz
(AppI.) Tj
100 Tz
1 0 0 1 222 203 Tm
(Physics) Tj
/F10 10 Tf
1 0 0 1 254 203 Tm
(45,) Tj
/F9 10 Tf
1 0 0 1 272 203 Tm
(No.) Tj
1 0 0 1 292 203 Tm
92 Tz
(12,) Tj
100 Tz
1 0 0 1 309 203 Tm
105 Tz
(5406-5421\(1974\).) Tj
100 Tz
/F1 10 Tf
1 0 0 1 102 188 Tm
(\[401) Tj
1 0 0 1 126 188 Tm
75 Tz
(N.L.) Tj
100 Tz
1 0 0 1 153 188 Tm
73 Tz
(Schryer,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 197 188 Tm
(\203An) Tj
1 0 0 1 222 188 Tm
107 Tz
(Extrapolation) Tj
100 Tz
1 0 0 1 288 188 Tm
103 Tz
(Step-Size) Tj
100 Tz
1 0 0 1 336 188 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 359 188 Tm
108 Tz
(Order) Tj
100 Tz
1 0 0 1 393 188 Tm
106 Tz
(Monitor) Tj
100 Tz
1 0 0 1 436 188 Tm
108 Tz
(for) Tj
100 Tz
/F1 10 Tf
1 0 0 1 456 188 Tm
72 Tz
(use) Tj
100 Tz
1 0 0 1 478 188 Tm
58 Tz
(in) Tj
100 Tz
1 0 0 1 493 188 Tm
74 Tz
(Solving) Tj
100 Tz
/F9 10 Tf
1 0 0 1 126 176 Tm
104 Tz
(Differential) Tj
100 Tz
1 0 0 1 179 176 Tm
104 Tz
(Equations\204,) Tj
100 Tz
1 0 0 1 233 176 Tm
106 Tz
(Proceedings) Tj
100 Tz
1 0 0 1 289 176 Tm
(ACM) Tj
1 0 0 1 317 176 Tm
103 Tz
(National) Tj
100 Tz
1 0 0 1 357 176 Tm
105 Tz
(Meeting,) Tj
100 Tz
1 0 0 1 399 176 Tm
(San) Tj
1 0 0 1 419 176 Tm
104 Tz
(Diego,) Tj
100 Tz
1 0 0 1 452 176 Tm
95 Tz
(1974.) Tj
100 Tz
1 0 0 1 102 161 Tm
(\[411) Tj
1 0 0 1 125 161 Tm
(N.L.) Tj
1 0 0 1 152 161 Tm
106 Tz
(Schryer,) Tj
100 Tz
1 0 0 1 196 161 Tm
(\203An) Tj
1 0 0 1 221 161 Tm
107 Tz
(Extrapolation) Tj
100 Tz
1 0 0 1 287 161 Tm
103 Tz
(Step-Size) Tj
100 Tz
1 0 0 1 335 161 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 359 161 Tm
104 Tz
(Order) Tj
100 Tz
1 0 0 1 392 161 Tm
106 Tz
(Monitor) Tj
100 Tz
1 0 0 1 435 161 Tm
(for) Tj
1 0 0 1 456 161 Tm
(use) Tj
1 0 0 1 478 161 Tm
(in) Tj
1 0 0 1 493 161 Tm
(Solving) Tj
1 0 0 1 125 149 Tm
104 Tz
(Differential) Tj
100 Tz
1 0 0 1 179 149 Tm
104 Tz
(Equations\204,) Tj
100 Tz
1 0 0 1 233 149 Tm
(in) Tj
1 0 0 1 244 149 Tm
104 Tz
(preparation.) Tj
100 Tz
1 0 0 1 101 133 Tm
(\[421) Tj
1 0 0 1 125 133 Tm
(N.L.) Tj
1 0 0 1 149 133 Tm
106 Tz
(Schryer,) Tj
100 Tz
1 0 0 1 189 133 Tm
91 Tz
(\203A) Tj
100 Tz
1 0 0 1 204 133 Tm
106 Tz
(Tutorial) Tj
100 Tz
1 0 0 1 243 133 Tm
(on) Tj
1 0 0 1 258 133 Tm
107 Tz
(Galerkin\202s) Tj
100 Tz
1 0 0 1 308 133 Tm
108 Tz
(Method,) Tj
100 Tz
1 0 0 1 349 133 Tm
105 Tz
(using) Tj
100 Tz
1 0 0 1 376 133 Tm
98 Tz
(B-~plines,) Tj
100 Tz
1 0 0 1 423 133 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 439 133 Tm
(Solving) Tj
1 0 0 1 476 133 Tm
104 Tz
(Differential) Tj
100 Tz
/F9 10 Tf
1 0 0 1 125 121 Tm
104 Tz
(Equations\204,) Tj
100 Tz
1 0 0 1 179 121 Tm
94 Tz
(Bell) Tj
100 Tz
1 0 0 1 199 121 Tm
107 Tz
(Laboratories) Tj
100 Tz
1 0 0 1 256 121 Tm
106 Tz
(Computing) Tj
100 Tz
1 0 0 1 308 121 Tm
(Science) Tj
1 0 0 1 344 121 Tm
105 Tz
(Technical) Tj
100 Tz
1 0 0 1 390 121 Tm
104 Tz
(Report) Tj
100 Tz
1 0 0 1 424 121 Tm
115 Tz
(#52,) Tj
100 Tz
1 0 0 1 450 121 Tm
95 Tz
(1976.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 101 106 Tm
(\[431) Tj
1 0 0 1 125 106 Tm
(M.H.) Tj
/F9 10 Tf
1 0 0 1 154 106 Tm
103 Tz
(Schultz,) Tj
100 Tz
1 0 0 1 195 106 Tm
105 Tz
(\203The) Tj
100 Tz
1 0 0 1 221 106 Tm
108 Tz
(Galerkin) Tj
100 Tz
1 0 0 1 266 106 Tm
106 Tz
(Method) Tj
100 Tz
1 0 0 1 306 106 Tm
(for) Tj
1 0 0 1 324 106 Tm
105 Tz
(Non-SeIf-Adjoint) Tj
100 Tz
1 0 0 1 407 106 Tm
104 Tz
(I\)ifferential) Tj
100 Tz
1 0 0 1 462 106 Tm
104 Tz
(Equations\204,) Tj
100 Tz
1 0 0 1 518 106 Tm
117 Tz
(I.) Tj
100 Tz
/F11 10 Tf
1 0 0 1 125 93 Tm
104 Tz
(Math.) Tj
100 Tz
1 0 0 1 154 93 Tm
91 Tz
(Arial.) Tj
100 Tz
1 0 0 1 180 93 Tm
(arid) Tj
1 0 0 1 199 93 Tm
95 Tz
(AppI.) Tj
100 Tz
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106 Tz
(very) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 624 Tm
107 Tz
(important) Tj
100 Tz
1 0 0 1 156 624 Tm
105 Tz
(decision.) Tj
100 Tz
1 0 0 1 207 624 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 233 624 Tm
104 Tz
(choice) Tj
100 Tz
1 0 0 1 269 624 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 288 624 Tm
108 Tz
(representation) Tj
100 Tz
1 0 0 1 359 624 Tm
104 Tz
(affects) Tj
100 Tz
1 0 0 1 396 624 Tm
(the) Tj
1 0 0 1 419 624 Tm
108 Tz
(entire) Tj
100 Tz
1 0 0 1 453 624 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 497 624 Tm
103 Tz
(process.) Tj
100 Tz
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1 0 0 1 104 611 Tm
(Specifically,) Tj
1 0 0 1 160 611 Tm
91 Tz
(we) Tj
100 Tz
1 0 0 1 175 611 Tm
(would) Tj
1 0 0 1 205 611 Tm
93 Tz
(like) Tj
100 Tz
1 0 0 1 225 611 Tm
(to) Tj
1 0 0 1 237 611 Tm
107 Tz
(choose) Tj
100 Tz
1 0 0 1 270 611 Tm
(a) Tj
1 0 0 1 279 611 Tm
(space) Tj
1 0 0 1 305 611 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 318 611 Tm
107 Tz
(functions,) Tj
100 Tz
1 0 0 1 366 611 Tm
108 Tz
(out) Tj
100 Tz
1 0 0 1 384 611 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 396 611 Tm
104 Tz
(which) Tj
100 Tz
1 0 0 1 425 611 Tm
(we) Tj
1 0 0 1 441 611 Tm
93 Tz
(will) Tj
100 Tz
1 0 0 1 460 611 Tm
91 Tz
(try) Tj
100 Tz
1 0 0 1 475 611 Tm
(to) Tj
1 0 0 1 487 611 Tm
104 Tz
(obtain) Tj
100 Tz
1 0 0 1 518 611 Tm
(the) Tj
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1 0 0 1 104 600 Tm
111 Tz
(element) Tj
100 Tz
1 0 0 1 144 600 Tm
104 Tz
(closest) Tj
100 Tz
1 0 0 1 177 600 Tm
(to) Tj
1 0 0 1 189 600 Tm
(the) Tj
1 0 0 1 206 600 Tm
106 Tz
(solution.) Tj
100 Tz
1 0 0 1 251 600 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 274 600 Tm
(space) Tj
1 0 0 1 301 600 Tm
107 Tz
(should) Tj
100 Tz
1 0 0 1 334 600 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 358 600 Tm
103 Tz
(several) Tj
100 Tz
1 0 0 1 393 600 Tm
(nice) Tj
1 0 0 1 414 600 Tm
107 Tz
(properties,) Tj
100 Tz
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105 Tz
(including) Tj
100 Tz
1 0 0 1 508 600 Tm
(being) Tj
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(\(I) Tj
1 0 0 1 115 588 Tm
33 Tz
(\)) Tj
100 Tz
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(easy) Tj
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(to) Tj
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(work) Tj
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106 Tz
(with) Tj
100 Tz
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(and) Tj
1 0 0 1 223 588 Tm
108 Tz
(\(2\)) Tj
100 Tz
1 0 0 1 239 588 Tm
103 Tz
(capable) Tj
100 Tz
1 0 0 1 275 588 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 288 588 Tm
106 Tz
(approximating) Tj
100 Tz
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1 0 0 1 354 588 Tm
(the) Tj
1 0 0 1 371 588 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 410 588 Tm
102 Tz
(accurately.) Tj
100 Tz
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1 0 0 1 129 572 Tm
(Such) Tj
1 0 0 1 157 572 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 168 572 Tm
108 Tz
(representation) Tj
100 Tz
1 0 0 1 236 572 Tm
108 Tz
(exists) Tj
100 Tz
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1 0 0 1 267 572 Tm
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1 0 0 1 276 572 Tm
107 Tz
(expansion) Tj
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1 0 0 1 326 572 Tm
(in) Tj
1 0 0 1 341 572 Tm
98 Tz
(B-sphines) Tj
100 Tz
1 0 0 1 386 572 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 401 572 Tm
105 Tz
(order) Tj
100 Tz
/F3 10 Tf
1 0 0 1 430 572 Tm
67 Tz
(k) Tj
100 Tz
/F1 10 Tf
1 0 0 1 443 572 Tm
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1 0 0 1 490 572 Tm
75 Tz
(This) Tj
100 Tz
1 0 0 1 515 572 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 527 572 Tm
50 Tz
(a) Tj
100 Tz
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1 0 0 1 105 559 Tm
106 Tz
(method) Tj
100 Tz
1 0 0 1 142 559 Tm
(for) Tj
1 0 0 1 158 559 Tm
108 Tz
(representing) Tj
100 Tz
1 0 0 1 216 559 Tm
107 Tz
(functions) Tj
100 Tz
1 0 0 1 261 559 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 274 559 Tm
102 Tz
(piecewise) Tj
100 Tz
1 0 0 1 319 559 Tm
106 Tz
(polynomials,) Tj
100 Tz
1 0 0 1 378 559 Tm
(that) Tj
1 0 0 1 399 559 Tm
89 Tz
(is,) Tj
100 Tz
1 0 0 1 412 559 Tm
104 Tz
(polynomials) Tj
100 Tz
1 0 0 1 468 559 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 480 559 Tm
104 Tz
(degree) Tj
100 Tz
1 0 0 1 513 559 Tm
89 Tz
(k\205I) Tj
100 Tz
1 0 0 1 105 548 Tm
(or) Tj
1 0 0 1 118 548 Tm
93 Tz
(less) Tj
100 Tz
1 0 0 1 137 548 Tm
111 Tz
(over) Tj
100 Tz
1 0 0 1 160 548 Tm
105 Tz
(each) Tj
100 Tz
1 0 0 1 184 548 Tm
108 Tz
(sub-interval) Tj
100 Tz
1 0 0 1 240 548 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 253 548 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 262 548 Tm
105 Tz
(mesh) Tj
100 Tz
1 0 0 1 289 548 Tm
(or) Tj
1 0 0 1 302 548 Tm
(grid.) Tj
1 0 0 1 329 548 Tm
110 Tz
(Ilere) Tj
100 Tz
1 0 0 1 355 548 Tm
(the) Tj
1 0 0 1 373 548 Tm
107 Tz
(integer) Tj
100 Tz
/F3 10 Tf
1 0 0 1 407 548 Tm
67 Tz
(k) Tj
100 Tz
/F1 10 Tf
1 0 0 1 418 548 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 428 548 Tm
78 Tz
(any) Tj
100 Tz
1 0 0 1 447 548 Tm
92 Tz
(number) Tj
100 Tz
/F3 10 Tf
1 0 0 1 486 548 Tm
67 Tz
(k) Tj
100 Tz
/F9 10 Tf
1 0 0 1 497 548 Tm
(~) Tj
/F9 10 Tf
1 0 0 1 509 548 Tm
60 Tz
(2) Tj
100 Tz
/F9 10 Tf
1 0 0 1 518 548 Tm
(the) Tj
/F9 10 Tf
1 0 0 1 105 536 Tm
111 Tz
(user) Tj
100 Tz
1 0 0 1 128 536 Tm
103 Tz
(desires.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 168 536 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 190 536 Tm
102 Tz
(piecewise) Tj
100 Tz
1 0 0 1 236 536 Tm
104 Tz
(polynomial) Tj
100 Tz
1 0 0 1 289 536 Tm
108 Tz
(representation) Tj
100 Tz
1 0 0 1 357 536 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 368 536 Tm
106 Tz
(required) Tj
100 Tz
1 0 0 1 409 536 Tm
(to) Tj
1 0 0 1 422 536 Tm
(satisfy) Tj
1 0 0 1 453 536 Tm
104 Tz
(certain) Tj
100 Tz
1 0 0 1 487 536 Tm
105 Tz
(continuity) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 524 Tm
106 Tz
(restrictions) Tj
100 Tz
1 0 0 1 158 524 Tm
(at) Tj
1 0 0 1 171 524 Tm
(the) Tj
1 0 0 1 190 524 Tm
107 Tz
(end) Tj
100 Tz
1 0 0 1 211 524 Tm
104 Tz
(points) Tj
100 Tz
1 0 0 1 242 524 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 256 524 Tm
89 Tz
(each) Tj
100 Tz
1 0 0 1 282 524 Tm
90 Tz
(mesh) Tj
100 Tz
1 0 0 1 310 524 Tm
107 Tz
(sub-interval.) Tj
100 Tz
1 0 0 1 373 524 Tm
98 Tz
(Specihically,) Tj
100 Tz
1 0 0 1 430 524 Tm
90 Tz
(let) Tj
100 Tz
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1 0 0 1 446 524 Tm
(~) Tj
/F5 5 Tf
1 0 0 1 455 524 Tm
167 Tz
(=) Tj
100 Tz
/F12 7 Tf
1 0 0 1 465 524 Tm
110 Tz
(\(XI) Tj
100 Tz
/F11 11 Tf
1 0 0 1 479 524 Tm
50 Tz
(,) Tj
100 Tz
/F5 4 Tf
1 0 0 1 494 524 Tm
(\206) Tj
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1 0 0 1 105 512 Tm
104 Tz
(where) Tj
100 Tz
/F11 11 Tf
1 0 0 1 135 512 Tm
108 Tz
(L=x~) Tj
100 Tz
1 0 0 1 168 512 Tm
200 Tz
(=) Tj
100 Tz
1 0 0 1 180 512 Tm
112 Tz
(x,) Tj
100 Tz
1 0 0 1 194 512 Tm
157 Tz
(\() Tj
100 Tz
1 0 0 1 233 512 Tm
157 Tz
(\() Tj
100 Tz
/F12 9 Tf
1 0 0 1 245 512 Tm
124 Tz
(XN=R,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 284 512 Tm
67 Tz
(be) Tj
100 Tz
1 0 0 1 298 512 Tm
50 Tz
(a) Tj
100 Tz
/F9 10 Tf
1 0 0 1 307 512 Tm
(grid) Tj
1 0 0 1 329 512 Tm
(on) Tj
1 0 0 1 345 512 Tm
(the) Tj
1 0 0 1 363 512 Tm
103 Tz
(interval) Tj
100 Tz
1 0 0 1 401 512 Tm
111 Tz
(\(L,R\).) Tj
100 Tz
1 0 0 1 437 512 Tm
(Let) Tj
/F3 10 Tf
1 0 0 1 456 512 Tm
67 Tz
(m,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 471 512 Tm
67 Tz
(be) Tj
100 Tz
1 0 0 1 486 512 Tm
67 Tz
(the) Tj
100 Tz
/F10 10 Tf
1 0 0 1 503 512 Tm
119 Tz
(multi) Tj
100 Tz
(-) Tj
1 0 0 1 104 500 Tm
104 Tz
(plicity) Tj
100 Tz
/F9 10 Tf
1 0 0 1 137 500 Tm
111 Tz
(of) Tj
100 Tz
/F12 8 Tf
1 0 0 1 149 500 Tm
120 Tz
(x,,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 164 500 Tm
(or) Tj
1 0 0 1 177 500 Tm
(the) Tj
1 0 0 1 194 500 Tm
109 Tz
(number) Tj
100 Tz
1 0 0 1 232 500 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 245 500 Tm
105 Tz
(times) Tj
100 Tz
/F12 9 Tf
1 0 0 1 272 500 Tm
114 Tz
(x,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 284 500 Tm
106 Tz
(appears) Tj
100 Tz
1 0 0 1 321 500 Tm
(in) Tj
1 0 0 1 333 500 Tm
(the) Tj
1 0 0 1 350 500 Tm
(list) Tj
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(ir.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 383 500 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 404 500 Tm
(space) Tj
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111 Tz
(of) Tj
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1 0 0 1 443 500 Tm
103 Tz
(B-splines) Tj
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111 Tz
(of) Tj
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1 0 0 1 498 500 Tm
105 Tz
(order) Tj
100 Tz
/F11 9 Tf
1 0 0 1 525 500 Tm
125 Tz
(k) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 488 Tm
106 Tz
(defined) Tj
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1 0 0 1 140 488 Tm
(on) Tj
1 0 0 1 155 488 Tm
(the) Tj
1 0 0 1 173 488 Tm
105 Tz
(mesh) Tj
100 Tz
/F10 8 Tf
1 0 0 1 199 488 Tm
86 Tz
(iT) Tj
100 Tz
/F9 10 Tf
1 0 0 1 210 488 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 220 488 Tm
106 Tz
(defined) Tj
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1 0 0 1 256 488 Tm
(to) Tj
1 0 0 1 268 488 Tm
(be) Tj
1 0 0 1 282 488 Tm
(the) Tj
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105 Tz
(collection) Tj
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1 0 0 1 344 488 Tm
111 Tz
(of) Tj
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1 0 0 1 356 488 Tm
90 Tz
(all) Tj
100 Tz
1 0 0 1 370 488 Tm
107 Tz
(functions) Tj
100 Tz
/F11 13 Tf
1 0 0 1 414 488 Tm
157 Tz
(f) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 473 Tm
130 Tz
(\(All\)) Tj
100 Tz
1 0 0 1 139 473 Tm
(which) Tj
1 0 0 1 168 473 Tm
(are) Tj
1 0 0 1 185 473 Tm
104 Tz
(polynomials) Tj
100 Tz
1 0 0 1 241 473 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 253 473 Tm
104 Tz
(degree) Tj
100 Tz
1 0 0 1 287 473 Tm
129 Tz
(\<) Tj
100 Tz
/F3 10 Tf
1 0 0 1 299 473 Tm
67 Tz
(k) Tj
100 Tz
/F9 10 Tf
1 0 0 1 309 473 Tm
(on) Tj
1 0 0 1 324 473 Tm
(each) Tj
1 0 0 1 347 473 Tm
106 Tz
(interval) Tj
100 Tz
/F12 9 Tf
1 0 0 1 384 473 Tm
125 Tz
(\(x,) Tj
100 Tz
1 0 0 1 400 473 Tm
105 Tz
(,x,~) Tj
-5 Ts

(1) Tj
100 Tz
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1 0 0 1 424 473 Tm
-5 Ts
33 Tz
(\)) Tj
100 Tz
1 0 0 1 431 473 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 448 473 Tm
115 Tz
(i=l) Tj
100 Tz
1 0 0 1 494 473 Tm
(N\205I,) Tj
/F7 7 Tf
1 0 0 1 192 461 Tm
96 Tz
(k\205I\205rn) Tj
100 Tz
1 0 0 1 262 461 Tm
(k) Tj
1 0 0 1 273 461 Tm
(I) Tj
1 0 0 1 281 461 Tm
(m) Tj
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1 0 0 1 105 455 Tm
(\(A) Tj
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93 Tz
(1.2\)) Tj
100 Tz
1 0 0 1 139 455 Tm
(for) Tj
1 0 0 1 156 455 Tm
104 Tz
(which) Tj
100 Tz
/F11 11 Tf
1 0 0 1 186 455 Tm
(d) Tj
1 0 0 1 217 455 Tm
112 Tz
(\201f\(x,\)) Tj
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/F10 13 Tf
1 0 0 1 244 455 Tm
(/) Tj
/F11 11 Tf
1 0 0 1 251 455 Tm
(dx) Tj
/F6 4 Tf
1 0 0 1 267 455 Tm
(\205) Tj
1 0 0 1 276 455 Tm
(\205) Tj
/F12 4 Tf
1 0 0 1 286 455 Tm
(\201) Tj
/F9 10 Tf
1 0 0 1 293 455 Tm
108 Tz
(exists) Tj
100 Tz
1 0 0 1 321 455 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 342 455 Tm
(is) Tj
/F9 10 Tf
1 0 0 1 352 455 Tm
110 Tz
(continuous) Tj
100 Tz
1 0 0 1 405 455 Tm
(at) Tj
1 0 0 1 416 455 Tm
105 Tz
(each) Tj
100 Tz
/F12 9 Tf
1 0 0 1 441 455 Tm
110 Tz
(x,,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 456 455 Tm
108 Tz
(for) Tj
100 Tz
/F11 9 Tf
1 0 0 1 474 455 Tm
111 Tz
(i=) Tj
100 Tz
/F1 10 Tf
1 0 0 1 486 455 Tm
17 Tz
(I) Tj
100 Tz
/F11 11 Tf
1 0 0 1 520 455 Tm
(N.) Tj
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1 0 0 1 139 444 Tm
105 Tz
(when) Tj
100 Tz
1 0 0 1 166 444 Tm
103 Tz
(viewed) Tj
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1 0 0 1 199 444 Tm
(as) Tj
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75 Tz
(a) Tj
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1 0 0 1 220 444 Tm
106 Tz
(function) Tj
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1 0 0 1 260 444 Tm
106 Tz
(defined) Tj
100 Tz
1 0 0 1 295 444 Tm
106 Tz
(only) Tj
100 Tz
1 0 0 1 318 444 Tm
(on) Tj
/F11 11 Tf
1 0 0 1 333 444 Tm
(\[L,RI,) Tj
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1 0 0 1 367 444 Tm
107 Tz
(and) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 428 Tm
111 Tz
(\(AI.3\)) Tj
100 Tz
1 0 0 1 139 428 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 155 428 Tm
(which) Tj
/F11 13 Tf
1 0 0 1 184 428 Tm
157 Tz
(f) Tj
100 Tz
/F1 10 Tf
1 0 0 1 214 428 Tm
67 Tz
(0) Tj
100 Tz
1 0 0 1 223 428 Tm
74 Tz
(outside) Tj
100 Tz
/F11 11 Tf
1 0 0 1 259 428 Tm
(\[L,RI.) Tj
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1 0 0 1 129 413 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 151 413 Tm
104 Tz
(multiplicity) Tj
100 Tz
/F3 10 Tf
1 0 0 1 205 413 Tm
67 Tz
(m,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 220 413 Tm
(of) Tj
1 0 0 1 233 413 Tm
(a) Tj
1 0 0 1 242 413 Tm
105 Tz
(point) Tj
100 Tz
/F12 9 Tf
1 0 0 1 268 413 Tm
114 Tz
(x,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 281 413 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 292 413 Tm
65 Tz
(restricted) Tj
100 Tz
1 0 0 1 337 413 Tm
58 Tz
(to) Tj
100 Tz
1 0 0 1 350 413 Tm
67 Tz
(be) Tj
100 Tz
1 0 0 1 364 413 Tm
58 Tz
(in) Tj
100 Tz
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1 0 0 1 376 413 Tm
(the) Tj
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1 0 0 1 394 413 Tm
(range) Tj
1 0 0 1 424 413 Tm
33 Tz
(I) Tj
100 Tz
/F11 11 Tf
1 0 0 1 432 413 Tm
157 Tz
(\() Tj
100 Tz
1 0 0 1 444 413 Tm
80 Tz
(m,) Tj
100 Tz
1 0 0 1 459 413 Tm
157 Tz
(\() Tj
100 Tz
1 0 0 1 472 413 Tm
(k.) Tj
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1 0 0 1 489 413 Tm
107 Tz
(For) Tj
100 Tz
/F3 10 Tf
1 0 0 1 508 413 Tm
83 Tz
(m,=l) Tj
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/F9 10 Tf
1 0 0 1 105 400 Tm
91 Tz
(we) Tj
100 Tz
1 0 0 1 120 400 Tm
105 Tz
(have) Tj
100 Tz
/F11 10 Tf
1 0 0 1 144 400 Tm
130 Tz
(dk) Tj
5 Ts

(2) Tj
5 Ts

(f/dxA) Tj
5 Ts

(2) Tj
100 Tz
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1 0 0 1 207 400 Tm
5 Ts
110 Tz
(continuous) Tj
100 Tz
1 0 0 1 258 400 Tm
(at) Tj
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1 0 0 1 270 400 Tm
(x,.) Tj
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1 0 0 1 288 400 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 311 400 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 322 400 Tm
(the) Tj
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105 Tz
(most) Tj
100 Tz
1 0 0 1 363 400 Tm
107 Tz
(continuity) Tj
100 Tz
1 0 0 1 411 400 Tm
(which) Tj
1 0 0 1 440 400 Tm
(can) Tj
1 0 0 1 459 400 Tm
(be) Tj
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106 Tz
(imposed) Tj
100 Tz
1 0 0 1 512 400 Tm
(at) Tj
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1 0 0 1 524 400 Tm
86 Tz
(x,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 388 Tm
106 Tz
(without) Tj
100 Tz
1 0 0 1 143 388 Tm
103 Tz
(making) Tj
100 Tz
/F11 13 Tf
1 0 0 1 178 388 Tm
150 Tz
(f) Tj
100 Tz
/F1 10 Tf
1 0 0 1 190 388 Tm
50 Tz
(a) Tj
100 Tz
1 0 0 1 200 388 Tm
78 Tz
(polynomial) Tj
100 Tz
1 0 0 1 252 388 Tm
67 Tz
(of) Tj
100 Tz
1 0 0 1 266 388 Tm
78 Tz
(degree) Tj
100 Tz
1 0 0 1 300 388 Tm
89 Tz
(k\205I) Tj
100 Tz
1 0 0 1 323 388 Tm
83 Tz
(on) Tj
100 Tz
/F12 9 Tf
1 0 0 1 339 388 Tm
110 Tz
(\(x,) Tj
100 Tz
/F10 4 Tf
1 0 0 1 361 388 Tm
(.) Tj
/F4 7 Tf
1 0 0 1 366 388 Tm
88 Tz
(X;~) Tj
-5 Ts

(1) Tj
-5 Ts

(\).) Tj
100 Tz
/F1 10 Tf
1 0 0 1 399 388 Tm
78 Tz
(For) Tj
100 Tz
/F11 11 Tf
1 0 0 1 419 388 Tm
80 Tz
(m,) Tj
100 Tz
/F5 5 Tf
1 0 0 1 431 388 Tm
167 Tz
(=) Tj
100 Tz
/F3 10 Tf
1 0 0 1 440 388 Tm
67 Tz
(k) Tj
100 Tz
/F1 10 Tf
1 0 0 1 451 388 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 469 388 Tm
74 Tz
(condition) Tj
100 Tz
1 0 0 1 515 388 Tm
67 Tz
(that) Tj
100 Tz
/F3 10 Tf
1 0 0 1 105 376 Tm
108 Tz
(d\202f/) Tj
100 Tz
/F9 10 Tf
1 0 0 1 134 376 Tm
77 Tz
(dx\205i) Tj
100 Tz
1 0 0 1 158 376 Tm
(be) Tj
1 0 0 1 172 376 Tm
110 Tz
(continuous) Tj
100 Tz
1 0 0 1 225 376 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 237 376 Tm
107 Tz
(interpreted) Tj
100 Tz
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(to) Tj
1 0 0 1 302 376 Tm
105 Tz
(mean) Tj
100 Tz
1 0 0 1 330 376 Tm
(that) Tj
/F11 13 Tf
1 0 0 1 350 376 Tm
150 Tz
(f) Tj
100 Tz
/F9 10 Tf
1 0 0 1 362 376 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 373 376 Tm
110 Tz
(continuous) Tj
100 Tz
1 0 0 1 426 376 Tm
105 Tz
(from) Tj
100 Tz
1 0 0 1 452 376 Tm
(the) Tj
1 0 0 1 470 376 Tm
105 Tz
(right) Tj
100 Tz
1 0 0 1 495 376 Tm
106 Tz
(\(but) Tj
100 Tz
1 0 0 1 518 376 Tm
108 Tz
(not) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 364 Tm
102 Tz
(necessarily) Tj
100 Tz
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105 Tz
(from) Tj
100 Tz
1 0 0 1 181 364 Tm
(the) Tj
1 0 0 1 199 364 Tm
(left\)) Tj
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(at) Tj
/F12 9 Tf
1 0 0 1 233 364 Tm
120 Tz
(x) Tj
100 Tz
/F5 5 Tf
1 0 0 1 243 364 Tm
167 Tz
(=) Tj
100 Tz
/F12 9 Tf
1 0 0 1 254 364 Tm
110 Tz
(x,,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 270 364 Tm
(for) Tj
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1 0 0 1 286 364 Tm
(x,) Tj
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129 Tz
(\<) Tj
100 Tz
/F11 11 Tf
1 0 0 1 311 364 Tm
110 Tz
(R,) Tj
100 Tz
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1 0 0 1 327 364 Tm
107 Tz
(and) Tj
100 Tz
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110 Tz
(continuous) Tj
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105 Tz
(from) Tj
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(the) Tj
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(left) Tj
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83 Tz
(if) Tj
100 Tz
/F11 11 Tf
1 0 0 1 471 364 Tm
86 Tz
(x,) Tj
100 Tz
/F5 5 Tf
1 0 0 1 482 364 Tm
167 Tz
(=) Tj
100 Tz
/F11 11 Tf
1 0 0 1 493 364 Tm
110 Tz
(R.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 512 364 Tm
75 Tz
(This) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 352 Tm
104 Tz
(means) Tj
100 Tz
1 0 0 1 137 352 Tm
(that) Tj
1 0 0 1 159 352 Tm
103 Tz
(B-splines) Tj
100 Tz
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(are) Tj
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110 Tz
(continuous) Tj
100 Tz
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(at) Tj
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(the) Tj
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107 Tz
(end) Tj
100 Tz
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104 Tz
(points) Tj
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111 Tz
(of) Tj
100 Tz
1 0 0 1 369 352 Tm
(the) Tj
1 0 0 1 387 352 Tm
105 Tz
(mesh) Tj
100 Tz
1 0 0 1 414 352 Tm
105 Tz
(when) Tj
100 Tz
1 0 0 1 442 352 Tm
103 Tz
(viewed) Tj
100 Tz
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(as) Tj
1 0 0 1 491 352 Tm
105 Tz
(functions) Tj
100 Tz
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106 Tz
(defined) Tj
100 Tz
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(only) Tj
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(on) Tj
/F11 11 Tf
1 0 0 1 182 340 Tm
(\[L,RI.) Tj
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1 0 0 1 220 340 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 244 340 Tm
105 Tz
(collection) Tj
100 Tz
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111 Tz
(of) Tj
100 Tz
1 0 0 1 306 340 Tm
107 Tz
(functions) Tj
100 Tz
1 0 0 1 352 340 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 363 340 Tm
109 Tz
(denoted) Tj
100 Tz
1 0 0 1 403 340 Tm
62 Tz
(by\202) Tj
100 Tz
/F11 10 Tf
1 0 0 1 418 340 Tm
110 Tz
(Bffk.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 448 340 Tm
108 Tz
(These) Tj
100 Tz
/F11 11 Tf
1 0 0 1 480 340 Tm
(Bffk) Tj
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1 0 0 1 504 340 Tm
(spaces) Tj
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1 0 0 1 105 328 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 131 328 Tm
108 Tz
(rather) Tj
100 Tz
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(nice) Tj
1 0 0 1 185 328 Tm
106 Tz
(approximation) Tj
100 Tz
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107 Tz
(properties,) Tj
100 Tz
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(as) Tj
1 0 0 1 320 328 Tm
111 Tz
(summed) Tj
100 Tz
1 0 0 1 363 328 Tm
90 Tz
(up) Tj
100 Tz
1 0 0 1 379 328 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 394 328 Tm
103 Tz
(deBoor) Tj
100 Tz
1 0 0 1 431 328 Tm
(\[21,) Tj
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(in) Tj
1 0 0 1 466 328 Tm
(the) Tj
1 0 0 1 484 328 Tm
(case) Tj
1 0 0 1 508 328 Tm
105 Tz
(when) Tj
100 Tz
/F5 5 Tf
1 0 0 1 121 315 Tm
167 Tz
(=) Tj
100 Tz
/F7 10 Tf
1 0 0 1 132 315 Tm
80 Tz
(k) Tj
100 Tz
/F5 5 Tf
1 0 0 1 141 315 Tm
167 Tz
(=) Tj
100 Tz
/F7 8 Tf
1 0 0 1 153 315 Tm
107 Tz
(inN.) Tj
100 Tz
/F10 10 Tf
1 0 0 1 105 292 Tm
(Theorem) Tj
1 0 0 1 148 292 Tm
60 Tz
(1) Tj
100 Tz
/F9 10 Tf
1 0 0 1 130 277 Tm
(Let) Tj
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1 0 0 1 148 277 Tm
150 Tz
(f) Tj
100 Tz
/F9 10 Tf
1 0 0 1 160 277 Tm
(be) Tj
1 0 0 1 175 277 Tm
(any) Tj
1 0 0 1 195 277 Tm
106 Tz
(function) Tj
100 Tz
1 0 0 1 236 277 Tm
106 Tz
(with) Tj
100 Tz
/F11 6 Tf
1 0 0 1 259 277 Tm
147 Tz
(flIll) Tj
100 Tz
/F9 10 Tf
1 0 0 1 280 277 Tm
106 Tz
(through) Tj
100 Tz
/F11 7 Tf
1 0 0 1 319 277 Tm
144 Tz
(fIkI) Tj
100 Tz
/F9 10 Tf
1 0 0 1 341 277 Tm
110 Tz
(continuous) Tj
100 Tz
1 0 0 1 394 277 Tm
(on) Tj
/F11 12 Tf
1 0 0 1 411 277 Tm
(\[L,RI,) Tj
/F9 10 Tf
1 0 0 1 446 277 Tm
104 Tz
(where) Tj
100 Tz
/F11 10 Tf
1 0 0 1 476 277 Tm
113 Tz
(f\202J\202) Tj
100 Tz
/F9 10 Tf
1 0 0 1 497 277 Tm
106 Tz
(denotes) Tj
100 Tz
1 0 0 1 105 265 Tm
(the) Tj
/F11 7 Tf
1 0 0 1 124 265 Tm
120 Tz
(Jth) Tj
100 Tz
/F9 10 Tf
1 0 0 1 142 265 Tm
107 Tz
(derivative) Tj
100 Tz
1 0 0 1 191 265 Tm
111 Tz
(of) Tj
100 Tz
/F11 13 Tf
1 0 0 1 205 265 Tm
125 Tz
(f.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 225 265 Tm
(Let) Tj
/F11 10 Tf
1 0 0 1 246 265 Tm
80 Tz
(h) Tj
100 Tz
/F5 5 Tf
1 0 0 1 253 265 Tm
171 Tz
(=) Tj
100 Tz
/F11 11 Tf
1 0 0 1 277 265 Tm
105 Tz
(Max) Tj
100 Tz
/F9 9 Tf
1 0 0 1 316 265 Tm
88 Tz
(X,+I) Tj
100 Tz
/F12 9 Tf
1 0 0 1 335 265 Tm
(\205x,) Tj
/F5 15 Tf
1 0 0 1 355 265 Tm
25 Tz
(I) Tj
100 Tz
/F9 10 Tf
1 0 0 1 363 265 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 380 265 Tm
(the) Tj
1 0 0 1 399 265 Tm
(largest) Tj
1 0 0 1 433 265 Tm
105 Tz
(mesh) Tj
100 Tz
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103 Tz
(interval) Tj
100 Tz
1 0 0 1 501 265 Tm
104 Tz
(length.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 105 248 Tm
92 Tz
(Then) Tj
100 Tz
1 0 0 1 131 248 Tm
70 Tz
(there) Tj
100 Tz
1 0 0 1 157 248 Tm
50 Tz
(is) Tj
100 Tz
1 0 0 1 167 248 Tm
75 Tz
(an) Tj
100 Tz
/F9 10 Tf
1 0 0 1 181 248 Tm
109 Tz
(element) Tj
100 Tz
1 0 0 1 219 248 Tm
(g) Tj
1 0 0 1 229 248 Tm
111 Tz
(of) Tj
100 Tz
/F11 10 Tf
1 0 0 1 241 248 Tm
112 Tz
(B~k) Tj
100 Tz
/F1 10 Tf
1 0 0 1 264 248 Tm
67 Tz
(so) Tj
100 Tz
1 0 0 1 277 248 Tm
63 Tz
(that) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 212 Tm
(for) Tj
1 0 0 1 122 212 Tm
(0) Tj
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1 0 0 1 132 212 Tm
157 Tz
(\() Tj
100 Tz
1 0 0 1 143 212 Tm
125 Tz
(j) Tj
100 Tz
/F9 10 Tf
1 0 0 1 153 212 Tm
(~) Tj
/F11 10 Tf
1 0 0 1 165 212 Tm
125 Tz
(k,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 180 212 Tm
104 Tz
(where) Tj
100 Tz
/F11 12 Tf
1 0 0 1 211 212 Tm
116 Tz
(C\(k,f\)) Tj
100 Tz
/F9 10 Tf
1 0 0 1 250 212 Tm
109 Tz
(represents) Tj
100 Tz
1 0 0 1 299 212 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 308 212 Tm
108 Tz
(constant) Tj
100 Tz
1 0 0 1 350 212 Tm
(which) Tj
1 0 0 1 380 212 Tm
109 Tz
(depends) Tj
100 Tz
1 0 0 1 420 212 Tm
(only) Tj
1 0 0 1 444 212 Tm
(upon) Tj
/F11 10 Tf
1 0 0 1 471 212 Tm
(k) Tj
/F9 10 Tf
1 0 0 1 482 212 Tm
(and) Tj
/F11 13 Tf
1 0 0 1 501 212 Tm
133 Tz
(f.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 517 212 Tm
(but) Tj
/F1 10 Tf
1 0 0 1 105 200 Tm
72 Tz
(not) Tj
100 Tz
/F3 10 Tf
1 0 0 1 123 200 Tm
58 Tz
(h.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 129 185 Tm
79 Tz
(That) Tj
100 Tz
1 0 0 1 154 185 Tm
44 Tz
(is,) Tj
100 Tz
1 0 0 1 168 185 Tm
67 Tz
(as) Tj
100 Tz
1 0 0 1 181 185 Tm
77 Tz
(h\205~0,) Tj
100 Tz
1 0 0 1 210 185 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 228 185 Tm
70 Tz
(error) Tj
100 Tz
1 0 0 1 254 185 Tm
58 Tz
(in) Tj
100 Tz
1 0 0 1 267 185 Tm
67 Tz
(the) Tj
100 Tz
/F9 10 Tf
1 0 0 1 285 185 Tm
(best) Tj
1 0 0 1 307 185 Tm
103 Tz
(B-spline) Tj
100 Tz
1 0 0 1 346 185 Tm
106 Tz
(approximation) Tj
100 Tz
1 0 0 1 414 185 Tm
(to) Tj
/F11 13 Tf
1 0 0 1 426 185 Tm
150 Tz
(f) Tj
100 Tz
/F1 10 Tf
1 0 0 1 437 185 Tm
75 Tz
(goes) Tj
100 Tz
1 0 0 1 461 185 Tm
58 Tz
(to) Tj
100 Tz
1 0 0 1 473 185 Tm
75 Tz
(zero) Tj
100 Tz
1 0 0 1 496 185 Tm
58 Tz
(like) Tj
100 Tz
/F3 10 Tf
1 0 0 1 517 185 Tm
67 Tz
(hA:) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 173 Tm
(the) Tj
1 0 0 1 122 173 Tm
105 Tz
(error) Tj
100 Tz
1 0 0 1 147 173 Tm
(in) Tj
1 0 0 1 159 173 Tm
(its) Tj
1 0 0 1 172 173 Tm
107 Tz
(derivative) Tj
100 Tz
1 0 0 1 219 173 Tm
106 Tz
(behaves) Tj
100 Tz
1 0 0 1 258 173 Tm
93 Tz
(like) Tj
100 Tz
/F3 10 Tf
1 0 0 1 278 173 Tm
110 Tz
(hkK) Tj
100 Tz
/F1 10 Tf
1 0 0 1 303 173 Tm
58 Tz
(etc.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 129 158 Tm
105 Tz
(Note) Tj
100 Tz
1 0 0 1 157 158 Tm
(that) Tj
1 0 0 1 179 158 Tm
107 Tz
(this) Tj
100 Tz
1 0 0 1 201 158 Tm
109 Tz
(theorem) Tj
100 Tz
1 0 0 1 244 158 Tm
104 Tz
(makes) Tj
100 Tz
1 0 0 1 277 158 Tm
(no) Tj
1 0 0 1 293 158 Tm
108 Tz
(assumption) Tj
100 Tz
1 0 0 1 348 158 Tm
108 Tz
(about) Tj
100 Tz
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(the) Tj
1 0 0 1 399 158 Tm
106 Tz
(relative) Tj
100 Tz
/F1 10 Tf
1 0 0 1 436 158 Tm
74 Tz
(spacing) Tj
100 Tz
1 0 0 1 473 158 Tm
75 Tz
(of) Tj
100 Tz
1 0 0 1 488 158 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 508 158 Tm
79 Tz
(mesh) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 145 Tm
104 Tz
(points) Tj
100 Tz
1 0 0 1 135 145 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 148 145 Tm
(n) Tj
1 0 0 1 160 145 Tm
(in) Tj
1 0 0 1 172 145 Tm
105 Tz
(order) Tj
100 Tz
1 0 0 1 199 145 Tm
(to) Tj
1 0 0 1 212 145 Tm
(get) Tj
/F3 10 Tf
1 0 0 1 230 145 Tm
67 Tz
(hk) Tj
100 Tz
/F9 10 Tf
1 0 0 1 245 145 Tm
109 Tz
(error.) Tj
100 Tz
1 0 0 1 277 145 Tm
88 Tz
(In) Tj
100 Tz
1 0 0 1 290 145 Tm
(many) Tj
1 0 0 1 318 145 Tm
107 Tz
(problems,) Tj
100 Tz
1 0 0 1 366 145 Tm
(the) Tj
1 0 0 1 383 145 Tm
(ability) Tj
1 0 0 1 414 145 Tm
(to) Tj
1 0 0 1 425 145 Tm
104 Tz
(grade) Tj
100 Tz
1 0 0 1 454 145 Tm
(the) Tj
1 0 0 1 471 145 Tm
105 Tz
(mesh) Tj
100 Tz
1 0 0 1 498 145 Tm
(with) Tj
1 0 0 1 521 145 Tm
125 Tz
(B) Tj
100 Tz
(-) Tj
/F9 10 Tf
1 0 0 1 105 133 Tm
107 Tz
(splines) Tj
100 Tz
1 0 0 1 137 133 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 157 133 Tm
93 Tz
(still) Tj
100 Tz
1 0 0 1 175 133 Tm
(get) Tj
/F3 10 Tf
1 0 0 1 193 133 Tm
67 Tz
(hA) Tj
100 Tz
/F9 10 Tf
1 0 0 1 207 133 Tm
110 Tz
(error) Tj
100 Tz
1 0 0 1 233 133 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 242 133 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 250 133 Tm
103 Tz
(decided) Tj
100 Tz
1 0 0 1 287 133 Tm
102 Tz
(advantage.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 129 118 Tm
(In) Tj
1 0 0 1 142 118 Tm
103 Tz
(practice,) Tj
100 Tz
/F11 10 Tf
1 0 0 1 183 118 Tm
120 Tz
(k) Tj
100 Tz
/F9 9 Tf
1 0 0 1 193 118 Tm
83 Tz
(is) Tj
100 Tz
/F9 10 Tf
1 0 0 1 204 118 Tm
103 Tz
(usually) Tj
100 Tz
1 0 0 1 238 118 Tm
105 Tz
(taken) Tj
100 Tz
1 0 0 1 266 118 Tm
(to) Tj
1 0 0 1 278 118 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 292 118 Tm
(4,) Tj
1 0 0 1 303 118 Tm
(6,) Tj
/F9 10 Tf
1 0 0 1 315 118 Tm
80 Tz
(8) Tj
100 Tz
/F1 10 Tf
1 0 0 1 324 118 Tm
67 Tz
(or) Tj
100 Tz
1 0 0 1 337 118 Tm
83 Tz
(even) Tj
100 Tz
1 0 0 1 363 118 Tm
56 Tz
(10.) Tj
100 Tz
1 0 0 1 378 118 Tm
81 Tz
(depending) Tj
100 Tz
/F9 9 Tf
1 0 0 1 427 118 Tm
110 Tz
(on) Tj
100 Tz
/F9 10 Tf
1 0 0 1 442 118 Tm
(what) Tj
1 0 0 1 466 118 Tm
(the) Tj
1 0 0 1 484 118 Tm
106 Tz
(function) Tj
100 Tz
/F11 13 Tf
1 0 0 1 524 118 Tm
140 Tz
(f) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 106 Tm
105 Tz
(looks) Tj
100 Tz
1 0 0 1 132 106 Tm
93 Tz
(like) Tj
100 Tz
1 0 0 1 152 106 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 173 106 Tm
94 Tz
(how) Tj
100 Tz
1 0 0 1 196 106 Tm
104 Tz
(much) Tj
100 Tz
1 0 0 1 224 106 Tm
103 Tz
(accuracy) Tj
100 Tz
1 0 0 1 266 106 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 277 106 Tm
106 Tz
(desired.) Tj
100 Tz
/F11 10 Tf
1 0 0 1 320 106 Tm
(k) Tj
/F9 10 Tf
1 0 0 1 331 106 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 342 106 Tm
103 Tz
(usually,) Tj
100 Tz
1 0 0 1 381 106 Tm
(but) Tj
1 0 0 1 399 106 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 418 106 Tm
(always,) Tj
1 0 0 1 454 106 Tm
105 Tz
(taken) Tj
100 Tz
1 0 0 1 482 106 Tm
(to) Tj
1 0 0 1 495 106 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 509 106 Tm
105 Tz
(even) Tj
100 Tz
/F9 10 Tf
1 0 0 1 105 93 Tm
107 Tz
(due) Tj
100 Tz
1 0 0 1 125 93 Tm
(to) Tj
1 0 0 1 138 93 Tm
(the) Tj
1 0 0 1 156 93 Tm
108 Tz
(rather) Tj
100 Tz
1 0 0 1 186 93 Tm
107 Tz
(natural) Tj
100 Tz
1 0 0 1 220 93 Tm
94 Tz
(way) Tj
100 Tz
1 0 0 1 241 93 Tm
(in) Tj
1 0 0 1 254 93 Tm
(which) Tj
1 0 0 1 283 93 Tm
105 Tz
(such) Tj
100 Tz
1 0 0 1 307 93 Tm
107 Tz
(splines) Tj
100 Tz
1 0 0 1 341 93 Tm
105 Tz
(arise) Tj
100 Tz
1 0 0 1 365 93 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 385 93 Tm
105 Tz
(their) Tj
100 Tz
1 0 0 1 409 93 Tm
107 Tz
(smoothing) Tj
100 Tz
1 0 0 1 460 93 Tm
107 Tz
(properties) Tj
100 Tz
1 0 0 1 507 93 Tm
105 Tz
(when) Tj
100 Tz
1 0 0 1 106 82 Tm
(used) Tj
1 0 0 1 131 82 Tm
(to) Tj
1 0 0 1 144 82 Tm
108 Tz
(approximate) Tj
100 Tz
1 0 0 1 204 82 Tm
107 Tz
(functions) Tj
100 Tz
1 0 0 1 250 82 Tm
105 Tz
(described) Tj
100 Tz
1 0 0 1 297 82 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 312 82 Tm
106 Tz
(discrete) Tj
100 Tz
1 0 0 1 351 82 Tm
106 Tz
(data) Tj
100 Tz
/F10 7 Tf
1 0 0 1 375 82 Tm
(\[21.) Tj
/F9 10 Tf
1 0 0 1 398 82 Tm
102 Tz
(Typically,) Tj
100 Tz
1 0 0 1 446 82 Tm
(the) Tj
1 0 0 1 466 82 Tm
105 Tz
(more) Tj
100 Tz
1 0 0 1 493 82 Tm
(accuracy) Tj
/F9 10 Tf
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(is) Tj
100 Tz
1 0 0 1 131 621 Tm
77 Tz
(given) Tj
100 Tz
1 0 0 1 159 621 Tm
58 Tz
(in) Tj
100 Tz
1 0 0 1 172 621 Tm
(\[121) Tj
1 0 0 1 193 621 Tm
78 Tz
(and) Tj
100 Tz
/F9 13 Tf
1 0 0 1 213 621 Tm
(\[31.) Tj
/F1 10 Tf
1 0 0 1 235 621 Tm
63 Tz
(Briefly,) Tj
100 Tz
1 0 0 1 271 621 Tm
92 Tz
(when) Tj
100 Tz
1 0 0 1 298 621 Tm
67 Tz
(the) Tj
100 Tz
/F9 10 Tf
1 0 0 1 316 621 Tm
105 Tz
(multiplicities) Tj
100 Tz
/F9 9 Tf
1 0 0 1 376 621 Tm
122 Tz
(of) Tj
100 Tz
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1 0 0 1 389 621 Tm
(the) Tj
1 0 0 1 406 621 Tm
94 Tz
(first) Tj
100 Tz
1 0 0 1 427 621 Tm
(and) Tj
1 0 0 1 446 621 Tm
(last) Tj
1 0 0 1 464 621 Tm
105 Tz
(mesh) Tj
100 Tz
1 0 0 1 491 621 Tm
104 Tz
(points) Tj
100 Tz
1 0 0 1 521 621 Tm
(are) Tj
/F9 10 Tf
1 0 0 1 108 609 Tm
106 Tz
(both) Tj
100 Tz
/F3 9 Tf
1 0 0 1 131 609 Tm
80 Tz
(k,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 144 609 Tm
67 Tz
(so) Tj
100 Tz
1 0 0 1 158 609 Tm
63 Tz
(that) Tj
100 Tz
/F5 5 Tf
1 0 0 1 153 591 Tm
167 Tz
(=) Tj
100 Tz
1 0 0 1 189 591 Tm
167 Tz
(=) Tj
100 Tz
/F11 7 Tf
1 0 0 1 199 591 Tm
112 Tz
(Xk) Tj
100 Tz
/F9 10 Tf
1 0 0 1 107 572 Tm
107 Tz
(and) Tj
100 Tz
/F8 7 Tf
1 0 0 1 139 554 Tm
132 Tz
(XNk+I) Tj
100 Tz
/F5 5 Tf
1 0 0 1 173 554 Tm
167 Tz
(=) Tj
100 Tz
1 0 0 1 209 554 Tm
167 Tz
(=) Tj
100 Tz
/F7 7 Tf
1 0 0 1 220 554 Tm
110 Tz
(XN) Tj
100 Tz
/F9 10 Tf
1 0 0 1 108 536 Tm
106 Tz
(then) Tj
100 Tz
1 0 0 1 131 536 Tm
(the) Tj
1 0 0 1 148 536 Tm
(main) Tj
1 0 0 1 173 536 Tm
107 Tz
(properties) Tj
100 Tz
1 0 0 1 220 536 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 233 536 Tm
(the) Tj
/F11 11 Tf
1 0 0 1 250 536 Tm
109 Tz
(B,\(x\)) Tj
100 Tz
/F9 10 Tf
1 0 0 1 278 536 Tm
(follow) Tj
/F9 10 Tf
1 0 0 1 108 510 Tm
(\(A) Tj
1 0 0 1 120 510 Tm
(1.4\)) Tj
1 0 0 1 142 510 Tm
105 Tz
(Each) Tj
100 Tz
/F11 11 Tf
1 0 0 1 168 510 Tm
89 Tz
(B,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 183 510 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 194 510 Tm
79 Tz
(non-zero) Tj
100 Tz
1 0 0 1 238 510 Tm
75 Tz
(only) Tj
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1 0 0 1 261 510 Tm
83 Tz
(on) Tj
100 Tz
/F11 11 Tf
1 0 0 1 278 510 Tm
90 Tz
(lx,) Tj
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/F3 9 Tf
1 0 0 1 292 510 Tm
75 Tz
(,X,+kl) Tj
100 Tz
/F9 10 Tf
1 0 0 1 323 510 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 344 510 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 355 510 Tm
102 Tz
(identically) Tj
100 Tz
1 0 0 1 404 510 Tm
(zero) Tj
1 0 0 1 427 510 Tm
107 Tz
(elsewhere,) Tj
100 Tz
1 0 0 1 478 510 Tm
(as) Tj
1 0 0 1 492 510 Tm
94 Tz
(well) Tj
100 Tz
1 0 0 1 513 510 Tm
(as) Tj
1 0 0 1 526 510 Tm
(at) Tj
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1 0 0 1 181 497 Tm
127 Tz
(x,) Tj
-5 Ts

(1) Tj
100 Tz
/F9 10 Tf
1 0 0 1 201 497 Tm
-5 Ts
(and) Tj
/F12 7 Tf
1 0 0 1 220 497 Tm
120 Tz
(X,+*+I) Tj
100 Tz
1 0 0 1 277 497 Tm
115 Tz
(XN,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 295 497 Tm
83 Tz
(even) Tj
100 Tz
/F9 10 Tf
1 0 0 1 320 497 Tm
(if) Tj
1 0 0 1 330 497 Tm
(they) Tj
1 0 0 1 352 497 Tm
(are) Tj
1 0 0 1 369 497 Tm
(in) Tj
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1 0 0 1 381 497 Tm
(\[x,.) Tj
/F3 10 Tf
1 0 0 1 394 497 Tm
62 Tz
(,X,+II.) Tj
100 Tz
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1 0 0 1 108 482 Tm
119 Tz
(\(AlS\)) Tj
100 Tz
1 0 0 1 141 482 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 162 482 Tm
106 Tz
(sum) Tj
100 Tz
/F11 11 Tf
1 0 0 1 184 482 Tm
103 Tz
(B) Tj
-5 Ts

(1) Tj
-5 Ts

(\(x\)+) Tj
100 Tz
/F10 7 Tf
1 0 0 1 234 482 Tm
50 Tz
(\206) Tj
100 Tz
/F11 11 Tf
1 0 0 1 239 482 Tm
127 Tz
(+B~\(x\)) Tj
100 Tz
/F1 10 Tf
1 0 0 1 290 482 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 300 482 Tm
65 Tz
(identically) Tj
100 Tz
1 0 0 1 347 482 Tm
71 Tz
(one.) Tj
100 Tz
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1 0 0 1 108 466 Tm
(\(A) Tj
1 0 0 1 121 466 Tm
93 Tz
(1.6\)) Tj
100 Tz
1 0 0 1 142 466 Tm
105 Tz
(Each) Tj
100 Tz
/F11 11 Tf
1 0 0 1 167 466 Tm
89 Tz
(B,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 180 466 Tm
104 Tz
(obeys) Tj
100 Tz
1 0 0 1 208 466 Tm
80 Tz
(0) Tj
100 Tz
/F11 11 Tf
1 0 0 1 217 466 Tm
157 Tz
(\() Tj
100 Tz
1 0 0 1 230 466 Tm
109 Tz
(B,\(x\)) Tj
100 Tz
/F1 10 Tf
1 0 0 1 261 466 Tm
(~) Tj
1 0 0 1 273 466 Tm
17 Tz
(I) Tj
100 Tz
1 0 0 1 280 466 Tm
82 Tz
(everywhere) Tj
100 Tz
/F9 10 Tf
1 0 0 1 334 466 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 354 466 Tm
105 Tz
(possesses) Tj
100 Tz
1 0 0 1 398 466 Tm
106 Tz
(only) Tj
100 Tz
1 0 0 1 420 466 Tm
(one) Tj
1 0 0 1 440 466 Tm
104 Tz
(maximum.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 131 451 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 153 451 Tm
107 Tz
(convergence) Tj
100 Tz
1 0 0 1 212 451 Tm
108 Tz
(result) Tj
100 Tz
1 0 0 1 241 451 Tm
(of) Tj
1 0 0 1 253 451 Tm
108 Tz
(Theorem) Tj
100 Tz
1 0 0 1 299 451 Tm
33 Tz
(I) Tj
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1 0 0 1 307 451 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 318 451 Tm
109 Tz
(independent) Tj
100 Tz
/F1 10 Tf
1 0 0 1 376 451 Tm
75 Tz
(of) Tj
100 Tz
1 0 0 1 390 451 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 408 451 Tm
65 Tz
(multiplicities) Tj
100 Tz
/F10 8 Tf
1 0 0 1 469 451 Tm
(in,) Tj
/F1 10 Tf
1 0 0 1 483 451 Tm
75 Tz
(of) Tj
100 Tz
1 0 0 1 497 451 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 514 451 Tm
75 Tz
(inte) Tj
100 Tz
(-) Tj
/F1 10 Tf
1 0 0 1 107 439 Tm
58 Tz
(rior) Tj
100 Tz
1 0 0 1 127 439 Tm
69 Tz
(points) Tj
100 Tz
/F12 9 Tf
1 0 0 1 157 439 Tm
114 Tz
(x,) Tj
100 Tz
/F10 10 Tf
1 0 0 1 170 439 Tm
67 Tz
(\() Tj
100 Tz
/F3 9 Tf
1 0 0 1 178 439 Tm
80 Tz
(k) Tj
100 Tz
1 0 0 1 189 439 Tm
129 Tz
(\<) Tj
100 Tz
1 0 0 1 202 439 Tm
40 Tz
(i) Tj
100 Tz
1 0 0 1 210 439 Tm
(~) Tj
1 0 0 1 222 439 Tm
124 Tz
(N\205k) Tj
100 Tz
/F9 10 Tf
1 0 0 1 249 439 Tm
67 Tz
(\)) Tj
100 Tz
/F9 9 Tf
1 0 0 1 257 439 Tm
122 Tz
(of) Tj
100 Tz
/F9 10 Tf
1 0 0 1 270 439 Tm
(the) Tj
1 0 0 1 288 439 Tm
104 Tz
(mesh.) Tj
100 Tz
1 0 0 1 321 439 Tm
103 Tz
(Usually,) Tj
100 Tz
1 0 0 1 361 439 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 377 439 Tm
109 Tz
(smooth) Tj
100 Tz
1 0 0 1 414 439 Tm
107 Tz
(functions) Tj
100 Tz
/F11 13 Tf
1 0 0 1 458 439 Tm
133 Tz
(f,) Tj
100 Tz
/F10 10 Tf
1 0 0 1 473 439 Tm
105 Tz
(m,=l) Tj
100 Tz
/F1 10 Tf
1 0 0 1 500 439 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 511 439 Tm
73 Tz
(taken) Tj
100 Tz
/F9 10 Tf
1 0 0 1 107 427 Tm
(for) Tj
1 0 0 1 123 427 Tm
90 Tz
(all) Tj
100 Tz
1 0 0 1 137 427 Tm
109 Tz
(these) Tj
100 Tz
1 0 0 1 163 427 Tm
106 Tz
(interior) Tj
100 Tz
1 0 0 1 200 427 Tm
67 Tz
(\() Tj
100 Tz
1 0 0 1 207 427 Tm
(that) Tj
1 0 0 1 227 427 Tm
89 Tz
(is,) Tj
100 Tz
1 0 0 1 241 427 Tm
104 Tz
(strictly) Tj
100 Tz
1 0 0 1 273 427 Tm
106 Tz
(between) Tj
100 Tz
1 0 0 1 313 427 Tm
83 Tz
(L) Tj
100 Tz
1 0 0 1 323 427 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 342 427 Tm
83 Tz
(R) Tj
100 Tz
/F1 10 Tf
1 0 0 1 353 427 Tm
33 Tz
(\)) Tj
100 Tz
1 0 0 1 361 427 Tm
92 Tz
(mesh) Tj
100 Tz
1 0 0 1 388 427 Tm
64 Tz
(points.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 131 412 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 152 412 Tm
107 Tz
(end) Tj
100 Tz
1 0 0 1 173 412 Tm
104 Tz
(points) Tj
100 Tz
1 0 0 1 203 412 Tm
(of) Tj
1 0 0 1 216 412 Tm
(the) Tj
1 0 0 1 234 412 Tm
105 Tz
(mesh) Tj
100 Tz
1 0 0 1 262 412 Tm
97 Tz
(typically) Tj
100 Tz
1 0 0 1 301 412 Tm
105 Tz
(have) Tj
100 Tz
1 0 0 1 326 412 Tm
104 Tz
(multiplicity) Tj
100 Tz
/F11 10 Tf
1 0 0 1 380 412 Tm
120 Tz
(k) Tj
100 Tz
/F9 10 Tf
1 0 0 1 390 412 Tm
105 Tz
(since) Tj
100 Tz
1 0 0 1 416 412 Tm
(the) Tj
1 0 0 1 434 412 Tm
106 Tz
(function) Tj
100 Tz
/F11 13 Tf
1 0 0 1 474 412 Tm
150 Tz
(f) Tj
100 Tz
/F9 10 Tf
1 0 0 1 486 412 Tm
(usually) Tj
1 0 0 1 520 412 Tm
(has) Tj
/F11 12 Tf
1 0 0 1 106 399 Tm
122 Tz
(f\(L\)) Tj
100 Tz
/F10 10 Tf
1 0 0 1 135 399 Tm
200 Tz
(!=) Tj
100 Tz
1 0 0 1 148 399 Tm
80 Tz
(0) Tj
100 Tz
1 0 0 1 157 399 Tm
94 Tz
(and) Tj
100 Tz
/F11 11 Tf
1 0 0 1 177 399 Tm
126 Tz
(f\(R\)) Tj
100 Tz
1 0 0 1 207 399 Tm
200 Tz
(!=) Tj
100 Tz
/F9 10 Tf
1 0 0 1 219 399 Tm
(0,) Tj
1 0 0 1 232 399 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 253 399 Tm
(the) Tj
1 0 0 1 271 399 Tm
110 Tz
(elements) Tj
100 Tz
1 0 0 1 315 399 Tm
111 Tz
(of) Tj
100 Tz
/F11 10 Tf
1 0 0 1 329 399 Tm
112 Tz
(B~k) Tj
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/F1 10 Tf
1 0 0 1 352 399 Tm
78 Tz
(cannot) Tj
100 Tz
1 0 0 1 386 399 Tm
75 Tz
(be) Tj
100 Tz
/F9 9 Tf
1 0 0 1 401 399 Tm
118 Tz
(non-zero) Tj
100 Tz
1 0 0 1 445 399 Tm
114 Tz
(at) Tj
100 Tz
/F11 11 Tf
1 0 0 1 457 399 Tm
(L) Tj
/F9 10 Tf
1 0 0 1 470 399 Tm
107 Tz
(and) Tj
100 Tz
/F11 11 Tf
1 0 0 1 490 399 Tm
110 Tz
(R,) Tj
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/F1 10 Tf
1 0 0 1 507 399 Tm
72 Tz
(unless) Tj
100 Tz
/F12 7 Tf
1 0 0 1 108 387 Tm
(in) Tj
-5 Ts

(1) Tj
/F5 5 Tf
1 0 0 1 121 387 Tm
-5 Ts
171 Tz
(=) Tj
100 Tz
/F11 10 Tf
1 0 0 1 131 387 Tm
120 Tz
(k) Tj
100 Tz
/F5 5 Tf
1 0 0 1 139 387 Tm
167 Tz
(=) Tj
100 Tz
/F7 7 Tf
1 0 0 1 149 387 Tm
117 Tz
(inN) Tj
100 Tz
/F9 10 Tf
1 0 0 1 166 387 Tm
106 Tz
(because) Tj
100 Tz
/F1 10 Tf
1 0 0 1 203 387 Tm
75 Tz
(of) Tj
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1 0 0 1 217 387 Tm
83 Tz
(\(A) Tj
100 Tz
1 0 0 1 229 387 Tm
63 Tz
(1.2\)) Tj
100 Tz
1 0 0 1 250 387 Tm
83 Tz
(and) Tj
100 Tz
1 0 0 1 269 387 Tm
83 Tz
(\(A) Tj
100 Tz
1 0 0 1 282 387 Tm
60 Tz
(1.3\).) Tj
100 Tz
1 0 0 1 309 387 Tm
67 Tz
(ln) Tj
100 Tz
/F9 10 Tf
1 0 0 1 322 387 Tm
(fact,) Tj
1 0 0 1 344 387 Tm
106 Tz
(relations) Tj
100 Tz
1 0 0 1 385 387 Tm
107 Tz
(\(Al) Tj
100 Tz
1 0 0 1 403 387 Tm
111 Tz
(.2\)-\(A) Tj
100 Tz
1 0 0 1 432 387 Tm
93 Tz
(1.5\)) Tj
100 Tz
1 0 0 1 452 387 Tm
(show) Tj
1 0 0 1 478 387 Tm
(that) Tj
1 0 0 1 499 387 Tm
(the) Tj
1 0 0 1 515 387 Tm
106 Tz
(only) Tj
100 Tz
/F11 11 Tf
1 0 0 1 107 375 Tm
89 Tz
(B,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 120 375 Tm
104 Tz
(which) Tj
100 Tz
1 0 0 1 150 375 Tm
(are) Tj
1 0 0 1 167 375 Tm
108 Tz
(not) Tj
100 Tz
1 0 0 1 185 375 Tm
(zero) Tj
1 0 0 1 207 375 Tm
(at) Tj
/F11 11 Tf
1 0 0 1 219 375 Tm
83 Tz
(L) Tj
100 Tz
/F9 10 Tf
1 0 0 1 230 375 Tm
107 Tz
(and) Tj
100 Tz
/F11 11 Tf
1 0 0 1 250 375 Tm
(R) Tj
/F9 10 Tf
1 0 0 1 262 375 Tm
(are) Tj
/F11 11 Tf
1 0 0 1 279 375 Tm
67 Tz
(B) Tj
-5 Ts

(1) Tj
100 Tz
/F9 10 Tf
1 0 0 1 293 375 Tm
-5 Ts
107 Tz
(and) Tj
100 Tz
/F12 7 Tf
1 0 0 1 312 375 Tm
124 Tz
(BN..A,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 342 375 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 362 375 Tm
105 Tz
(these) Tj
100 Tz
1 0 0 1 388 375 Tm
104 Tz
(values) Tj
100 Tz
1 0 0 1 419 375 Tm
(are) Tj
1 0 0 1 436 375 Tm
(simply) Tj
/F11 11 Tf
1 0 0 1 469 375 Tm
67 Tz
(B) Tj
-5 Ts

(1) Tj
100 Tz
1 0 0 1 479 375 Tm
-5 Ts
107 Tz
(\(L\)) Tj
100 Tz
/F5 5 Tf
1 0 0 1 499 375 Tm
167 Tz
(=) Tj
100 Tz
/F1 10 Tf
1 0 0 1 511 375 Tm
17 Tz
(I) Tj
100 Tz
1 0 0 1 518 375 Tm
83 Tz
(and) Tj
100 Tz
/F8 7 Tf
1 0 0 1 107 363 Tm
141 Tz
(BNk\(R\)) Tj
100 Tz
/F5 5 Tf
1 0 0 1 152 363 Tm
167 Tz
(=) Tj
100 Tz
/F1 10 Tf
1 0 0 1 163 363 Tm
42 Tz
(I.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 132 347 Tm
114 Tz
(If) Tj
100 Tz
1 0 0 1 144 347 Tm
(the) Tj
1 0 0 1 161 347 Tm
106 Tz
(function) Tj
100 Tz
/F11 13 Tf
1 0 0 1 202 347 Tm
150 Tz
(f) Tj
100 Tz
/F9 10 Tf
1 0 0 1 214 347 Tm
(has) Tj
1 0 0 1 232 347 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 241 347 Tm
105 Tz
(discontinuity) Tj
100 Tz
1 0 0 1 302 347 Tm
(in) Tj
1 0 0 1 315 347 Tm
(its) Tj
/F11 6 Tf
1 0 0 1 328 347 Tm
130 Tz
(\}th) Tj
100 Tz
/F1 10 Tf
1 0 0 1 344 347 Tm
68 Tz
(derivative,) Tj
100 Tz
1 0 0 1 395 347 Tm
58 Tz
(at) Tj
100 Tz
/F12 9 Tf
1 0 0 1 407 347 Tm
110 Tz
(x,,) Tj
100 Tz
/F1 10 Tf
1 0 0 1 424 347 Tm
75 Tz
(then) Tj
100 Tz
/F10 8 Tf
1 0 0 1 448 347 Tm
(in,) Tj
/F5 5 Tf
1 0 0 1 460 347 Tm
167 Tz
(=) Tj
100 Tz
/F3 10 Tf
1 0 0 1 470 347 Tm
94 Tz
(k\205I) Tj
100 Tz
/F1 10 Tf
1 0 0 1 493 347 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 504 347 Tm
81 Tz
(chosen) Tj
100 Tz
/F1 10 Tf
1 0 0 1 107 335 Tm
79 Tz
(because) Tj
100 Tz
1 0 0 1 146 335 Tm
63 Tz
(this) Tj
100 Tz
1 0 0 1 165 335 Tm
72 Tz
(allows) Tj
100 Tz
1 0 0 1 197 335 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 215 335 Tm
81 Tz
(elements) Tj
100 Tz
1 0 0 1 259 335 Tm
75 Tz
(of) Tj
100 Tz
/F11 11 Tf
1 0 0 1 273 335 Tm
70 Tz
(BITA) Tj
100 Tz
/F1 10 Tf
1 0 0 1 296 335 Tm
58 Tz
(to) Tj
100 Tz
1 0 0 1 310 335 Tm
79 Tz
(have) Tj
100 Tz
/F1 10 Tf
1 0 0 1 335 335 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 353 335 Tm
88 Tz
(same) Tj
100 Tz
1 0 0 1 380 335 Tm
72 Tz
(behavior.) Tj
100 Tz
1 0 0 1 428 335 Tm
58 Tz
(If) Tj
100 Tz
1 0 0 1 439 335 Tm
67 Tz
(a) Tj
100 Tz
1 0 0 1 448 335 Tm
74 Tz
(smaller) Tj
100 Tz
1 0 0 1 485 335 Tm
67 Tz
(multiplicity) Tj
100 Tz
/F9 10 Tf
1 0 0 1 107 323 Tm
105 Tz
(were) Tj
100 Tz
1 0 0 1 131 323 Tm
106 Tz
(chosen,) Tj
100 Tz
1 0 0 1 170 323 Tm
(the) Tj
/F11 7 Tf
1 0 0 1 187 323 Tm
-5 Ts
120 Tz
(1) Tj
-5 Ts

(th) Tj
100 Tz
/F1 10 Tf
1 0 0 1 203 323 Tm
70 Tz
(derivative) Tj
100 Tz
1 0 0 1 250 323 Tm
75 Tz
(of) Tj
100 Tz
1 0 0 1 263 323 Tm
50 Tz
(all) Tj
100 Tz
1 0 0 1 278 323 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 295 323 Tm
81 Tz
(elements) Tj
100 Tz
1 0 0 1 339 323 Tm
75 Tz
(of) Tj
100 Tz
/F11 10 Tf
1 0 0 1 353 323 Tm
112 Tz
(B~k) Tj
100 Tz
/F9 10 Tf
1 0 0 1 376 323 Tm
(would) Tj
1 0 0 1 407 323 Tm
(be) Tj
1 0 0 1 420 323 Tm
110 Tz
(continuous) Tj
100 Tz
1 0 0 1 473 323 Tm
(at) Tj
/F12 9 Tf
1 0 0 1 485 323 Tm
110 Tz
(x,,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 501 323 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 521 323 Tm
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85 Tz
(u~,) Tj
100 Tz
1 0 0 1 218 508 Tm
80 Tz
(u) Tj
100 Tz
/F12 5 Tf
1 0 0 1 225 508 Tm
(~,,) Tj
/F10 10 Tf
1 0 0 1 238 508 Tm
(v,) Tj
1 0 0 1 250 508 Tm
(v,) Tj
1 0 0 1 263 508 Tm
92 Tz
(are) Tj
100 Tz
1 0 0 1 280 508 Tm
90 Tz
(all) Tj
100 Tz
1 0 0 1 295 508 Tm
102 Tz
(functions) Tj
100 Tz
1 0 0 1 340 508 Tm
111 Tz
(of) Tj
100 Tz
/F12 9 Tf
1 0 0 1 354 508 Tm
120 Tz
(x) Tj
100 Tz
/F9 10 Tf
1 0 0 1 364 508 Tm
105 Tz
(alone) Tj
100 Tz
1 0 0 1 393 508 Tm
107 Tz
(\(no) Tj
100 Tz
1 0 0 1 412 508 Tm
106 Tz
(dependence) Tj
100 Tz
1 0 0 1 469 508 Tm
(on) Tj
/F10 8 Tf
1 0 0 1 485 508 Tm
122 Tz
(t\).) Tj
100 Tz
/F9 10 Tf
1 0 0 1 504 508 Tm
(In) Tj
1 0 0 1 518 508 Tm
(this) Tj
/F9 10 Tf
1 0 0 1 105 497 Tm
(case) Tj
1 0 0 1 129 497 Tm
(POST) Tj
1 0 0 1 159 497 Tm
107 Tz
(should) Tj
100 Tz
1 0 0 1 193 497 Tm
107 Tz
(run) Tj
100 Tz
1 0 0 1 213 497 Tm
104 Tz
(substantially) Tj
100 Tz
1 0 0 1 272 497 Tm
104 Tz
(faster) Tj
100 Tz
1 0 0 1 302 497 Tm
106 Tz
(because) Tj
100 Tz
1 0 0 1 341 497 Tm
(the) Tj
1 0 0 1 359 497 Tm
106 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 402 497 Tm
110 Tz
(need) Tj
100 Tz
1 0 0 1 427 497 Tm
(only) Tj
1 0 0 1 452 497 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 466 497 Tm
107 Tz
(computed) Tj
100 Tz
/F11 11 Tf
1 0 0 1 515 497 Tm
90 Tz
(once) Tj
100 Tz
/F9 10 Tf
1 0 0 1 106 484 Tm
104 Tz
(during) Tj
100 Tz
1 0 0 1 138 484 Tm
(the) Tj
1 0 0 1 155 484 Tm
108 Tz
(entire) Tj
100 Tz
1 0 0 1 184 484 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 223 484 Tm
103 Tz
(process.) Tj
100 Tz
/F9 10 Tf
1 0 0 1 131 469 Tm
107 Tz
(For) Tj
100 Tz
1 0 0 1 150 469 Tm
107 Tz
(nonlinear) Tj
100 Tz
1 0 0 1 196 469 Tm
107 Tz
(problems,) Tj
100 Tz
1 0 0 1 243 469 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 252 469 Tm
109 Tz
(scheme) Tj
100 Tz
1 0 0 1 288 469 Tm
93 Tz
(will) Tj
100 Tz
1 0 0 1 308 469 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 323 469 Tm
107 Tz
(implemented) Tj
100 Tz
1 0 0 1 384 469 Tm
(for) Tj
1 0 0 1 401 469 Tm
106 Tz
(keeping) Tj
100 Tz
1 0 0 1 439 469 Tm
(an) Tj
1 0 0 1 454 469 Tm
90 Tz
(\203old\204) Tj
100 Tz
1 0 0 1 479 469 Tm
105 Tz
(value) Tj
100 Tz
1 0 0 1 506 469 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 519 469 Tm
(the) Tj
/F9 10 Tf
1 0 0 1 106 457 Tm
106 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 147 457 Tm
106 Tz
(over) Tj
100 Tz
1 0 0 1 171 457 Tm
(as) Tj
1 0 0 1 184 457 Tm
(many) Tj
1 0 0 1 212 457 Tm
107 Tz
(time-steps) Tj
100 Tz
1 0 0 1 261 457 Tm
(as) Tj
1 0 0 1 275 457 Tm
(the) Tj
1 0 0 1 292 457 Tm
106 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 333 457 Tm
107 Tz
(can) Tj
100 Tz
1 0 0 1 352 457 Tm
103 Tz
(provide) Tj
100 Tz
1 0 0 1 389 457 Tm
(an) Tj
1 0 0 1 404 457 Tm
106 Tz
(effective) Tj
100 Tz
1 0 0 1 445 457 Tm
105 Tz
(quasi-Newton) Tj
100 Tz
1 0 0 1 510 457 Tm
123 Tz
(itera) Tj
100 Tz
(-) Tj
1 0 0 1 106 445 Tm
93 Tz
(tive) Tj
100 Tz
1 0 0 1 127 445 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 167 445 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 182 445 Tm
(the) Tj
1 0 0 1 200 445 Tm
107 Tz
(nonlinear) Tj
100 Tz
1 0 0 1 246 445 Tm
107 Tz
(equations.) Tj
100 Tz
1 0 0 1 299 445 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 323 445 Tm
109 Tz
(scheme) Tj
100 Tz
1 0 0 1 361 445 Tm
93 Tz
(will) Tj
100 Tz
1 0 0 1 382 445 Tm
(use) Tj
1 0 0 1 401 445 Tm
(the) Tj
1 0 0 1 420 445 Tm
(fact) Tj
1 0 0 1 441 445 Tm
106 Tz
(that,) Tj
100 Tz
1 0 0 1 466 445 Tm
(in) Tj
1 0 0 1 478 445 Tm
109 Tz
(general,) Tj
100 Tz
1 0 0 1 519 445 Tm
(the) Tj
1 0 0 1 105 432 Tm
107 Tz
(convergence) Tj
100 Tz
1 0 0 1 165 432 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 180 432 Tm
75 Tz
(a) Tj
100 Tz
/F9 10 Tf
1 0 0 1 189 432 Tm
105 Tz
(quasi-Newton) Tj
100 Tz
1 0 0 1 255 432 Tm
106 Tz
(method) Tj
100 Tz
1 0 0 1 294 432 Tm
82 Tz
(with) Tj
100 Tz
1 0 0 1 318 432 Tm
(an) Tj
1 0 0 1 333 432 Tm
104 Tz
(\203out-of-date\204) Tj
100 Tz
1 0 0 1 396 432 Tm
106 Tz
(\(inaccurate\)) Tj
100 Tz
1 0 0 1 453 432 Tm
106 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 497 432 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 508 432 Tm
104 Tz
(linear) Tj
100 Tz
/F9 10 Tf
1 0 0 1 106 421 Tm
108 Tz
(rather) Tj
100 Tz
1 0 0 1 137 421 Tm
106 Tz
(than) Tj
100 Tz
1 0 0 1 161 421 Tm
105 Tz
(quadratic.) Tj
100 Tz
1 0 0 1 212 421 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 235 421 Tm
103 Tz
(possible) Tj
100 Tz
1 0 0 1 275 421 Tm
108 Tz
(run-time) Tj
100 Tz
1 0 0 1 318 421 Tm
109 Tz
(improvement) Tj
100 Tz
1 0 0 1 383 421 Tm
105 Tz
(using) Tj
100 Tz
1 0 0 1 410 421 Tm
105 Tz
(such) Tj
100 Tz
1 0 0 1 435 421 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 445 421 Tm
109 Tz
(scheme) Tj
100 Tz
1 0 0 1 483 421 Tm
(is) Tj
/F11 10 Tf
1 0 0 1 495 421 Tm
85 Tz
(krz~,) Tj
100 Tz
/F9 10 Tf
1 0 0 1 519 421 Tm
(the) Tj
1 0 0 1 106 408 Tm
(ratio) Tj
1 0 0 1 129 408 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 142 408 Tm
(the) Tj
1 0 0 1 159 408 Tm
(cost) Tj
1 0 0 1 180 408 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 193 408 Tm
107 Tz
(computing) Tj
100 Tz
1 0 0 1 243 408 Tm
(the) Tj
1 0 0 1 260 408 Tm
106 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 302 408 Tm
104 Tz
(\(9.18\)) Tj
100 Tz
/F9 10 Tf
1 0 0 1 333 408 Tm
(to) Tj
1 0 0 1 346 408 Tm
(the) Tj
1 0 0 1 363 408 Tm
(cost) Tj
1 0 0 1 384 408 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 396 408 Tm
107 Tz
(just) Tj
100 Tz
1 0 0 1 416 408 Tm
107 Tz
(computing) Tj
100 Tz
1 0 0 1 466 408 Tm
(the) Tj
1 0 0 1 483 408 Tm
115 Tz
(right-hand) Tj
100 Tz
(-) Tj
1 0 0 1 106 396 Tm
(side) Tj
1 0 0 1 127 396 Tm
107 Tz
(\(9.19\).) Tj
100 Tz
/F10 10 Tf
1 0 0 1 106 373 Tm
104 Tz
(Numerical) Tj
100 Tz
1 0 0 1 157 373 Tm
105 Tz
(Jacobians) Tj
100 Tz
/F9 10 Tf
1 0 0 1 131 357 Tm
109 Tz
(Another) Tj
100 Tz
1 0 0 1 173 357 Tm
103 Tz
(possible) Tj
100 Tz
1 0 0 1 214 357 Tm
107 Tz
(improvement) Tj
100 Tz
1 0 0 1 278 357 Tm
(would) Tj
1 0 0 1 310 357 Tm
(be) Tj
1 0 0 1 327 357 Tm
(the) Tj
1 0 0 1 345 357 Tm
107 Tz
(automatic) Tj
100 Tz
1 0 0 1 395 357 Tm
107 Tz
(numerical) Tj
100 Tz
1 0 0 1 443 357 Tm
107 Tz
(computation) Tj
100 Tz
1 0 0 1 504 357 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 519 357 Tm
(the) Tj
1 0 0 1 106 345 Tm
106 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 148 345 Tm
104 Tz
(matrix) Tj
100 Tz
1 0 0 1 180 345 Tm
105 Tz
(from) Tj
100 Tz
1 0 0 1 206 345 Tm
(the) Tj
1 0 0 1 224 345 Tm
104 Tz
(values) Tj
100 Tz
1 0 0 1 255 345 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 268 345 Tm
(a) Tj
1 0 0 1 277 345 Tm
107 Tz
(and) Tj
100 Tz
/F9 10 Tf
1 0 0 1 297 345 Tm
(f.) Tj
1 0 0 1 310 345 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 334 345 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 345 345 Tm
(not) Tj
/F9 10 Tf
1 0 0 1 363 345 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 372 345 Tm
104 Tz
(high-priority) Tj
100 Tz
1 0 0 1 431 345 Tm
106 Tz
(item) Tj
100 Tz
1 0 0 1 454 345 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 471 345 Tm
110 Tz
(three) Tj
100 Tz
1 0 0 1 498 345 Tm
103 Tz
(reasons.) Tj
100 Tz
1 0 0 1 106 333 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 127 333 Tm
(first) Tj
1 0 0 1 147 333 Tm
(is) Tj
1 0 0 1 158 333 Tm
106 Tz
(that) Tj
100 Tz
1 0 0 1 178 333 Tm
(it) Tj
1 0 0 1 188 333 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 198 333 Tm
103 Tz
(usually) Tj
100 Tz
1 0 0 1 232 333 Tm
(an) Tj
1 0 0 1 246 333 Tm
(easy) Tj
1 0 0 1 268 333 Tm
107 Tz
(matter) Tj
100 Tz
1 0 0 1 299 333 Tm
(for) Tj
1 0 0 1 316 333 Tm
(the) Tj
1 0 0 1 333 333 Tm
106 Tz
(user) Tj
100 Tz
1 0 0 1 355 333 Tm
(to) Tj
1 0 0 1 367 333 Tm
108 Tz
(compute,) Tj
100 Tz
1 0 0 1 411 333 Tm
90 Tz
(by) Tj
100 Tz
1 0 0 1 425 333 Tm
109 Tz
(hand,) Tj
100 Tz
1 0 0 1 454 333 Tm
(the) Tj
1 0 0 1 471 333 Tm
105 Tz
(necessary) Tj
100 Tz
1 0 0 1 516 333 Tm
125 Tz
(par) Tj
100 Tz
(-) Tj
/F9 10 Tf
1 0 0 1 106 321 Tm
(tial) Tj
1 0 0 1 123 321 Tm
104 Tz
(derivatives.) Tj
100 Tz
1 0 0 1 180 321 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 201 321 Tm
107 Tz
(second) Tj
100 Tz
1 0 0 1 235 321 Tm
104 Tz
(reason) Tj
100 Tz
1 0 0 1 267 321 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 278 321 Tm
(that) Tj
1 0 0 1 299 321 Tm
(the) Tj
1 0 0 1 316 321 Tm
(partial) Tj
/F9 10 Tf
1 0 0 1 346 321 Tm
107 Tz
(derivative) Tj
100 Tz
1 0 0 1 393 321 Tm
110 Tz
(generator) Tj
100 Tz
1 0 0 1 439 321 Tm
106 Tz
(PDGEN) Tj
100 Tz
1 0 0 1 480 321 Tm
(\[521) Tj
1 0 0 1 501 321 Tm
94 Tz
(may) Tj
100 Tz
1 0 0 1 523 321 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 106 309 Tm
105 Tz
(used) Tj
100 Tz
1 0 0 1 131 309 Tm
(to) Tj
1 0 0 1 144 309 Tm
105 Tz
(automatically) Tj
100 Tz
1 0 0 1 206 309 Tm
108 Tz
(compute) Tj
100 Tz
1 0 0 1 249 309 Tm
(the) Tj
1 0 0 1 267 309 Tm
106 Tz
(Jacobian) Tj
100 Tz
1 0 0 1 308 309 Tm
105 Tz
(when) Tj
100 Tz
1 0 0 1 337 309 Tm
80 Tz
(it) Tj
100 Tz
/F11 12 Tf
1 0 0 1 348 309 Tm
75 Tz
(is) Tj
100 Tz
/F9 10 Tf
1 0 0 1 358 309 Tm
(too) Tj
1 0 0 1 376 309 Tm
(difficult) Tj
1 0 0 1 415 309 Tm
(to) Tj
1 0 0 1 427 309 Tm
(do) Tj
1 0 0 1 443 309 Tm
80 Tz
(by) Tj
100 Tz
1 0 0 1 458 309 Tm
105 Tz
(hand.) Tj
100 Tz
1 0 0 1 490 309 Tm
106 Tz
(The) Tj
100 Tz
1 0 0 1 512 309 Tm
105 Tz
(third) Tj
100 Tz
/F9 10 Tf
1 0 0 1 106 297 Tm
104 Tz
(reason) Tj
100 Tz
1 0 0 1 139 297 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 150 297 Tm
(that) Tj
1 0 0 1 171 297 Tm
107 Tz
(numerical) Tj
100 Tz
1 0 0 1 218 297 Tm
107 Tz
(differentiation) Tj
100 Tz
1 0 0 1 285 297 Tm
83 Tz
(is) Tj
100 Tz
/F9 10 Tf
1 0 0 1 295 297 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 305 297 Tm
(\203black-art\204) Tj
1 0 0 1 354 297 Tm
108 Tz
(rather) Tj
100 Tz
1 0 0 1 384 297 Tm
106 Tz
(than) Tj
100 Tz
1 0 0 1 407 297 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 416 297 Tm
106 Tz
(science,) Tj
100 Tz
1 0 0 1 455 297 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 476 297 Tm
89 Tz
(its) Tj
100 Tz
1 0 0 1 490 297 Tm
(use) Tj
1 0 0 1 509 297 Tm
(could) Tj
1 0 0 1 106 285 Tm
106 Tz
(compromise) Tj
100 Tz
1 0 0 1 164 285 Tm
(the) Tj
1 0 0 1 182 285 Tm
107 Tz
(robustness) Tj
100 Tz
1 0 0 1 232 285 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 245 285 Tm
(POST.) Tj
1 0 0 1 281 285 Tm
106 Tz
(Anyone) Tj
100 Tz
1 0 0 1 320 285 Tm
104 Tz
(feeling) Tj
100 Tz
1 0 0 1 354 285 Tm
(that) Tj
1 0 0 1 375 285 Tm
105 Tz
(numerical) Tj
100 Tz
1 0 0 1 421 285 Tm
107 Tz
(Jacobians) Tj
100 Tz
1 0 0 1 467 285 Tm
(are) Tj
1 0 0 1 484 285 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 494 285 Tm
103 Tz
(necessity) Tj
100 Tz
/F9 10 Tf
1 0 0 1 106 273 Tm
107 Tz
(should) Tj
100 Tz
1 0 0 1 139 273 Tm
107 Tz
(contact) Tj
100 Tz
1 0 0 1 173 273 Tm
(the) Tj
1 0 0 1 190 273 Tm
107 Tz
(author,) Tj
100 Tz
1 0 0 1 225 273 Tm
108 Tz
(but) Tj
100 Tz
1 0 0 1 243 273 Tm
(be) Tj
1 0 0 1 257 273 Tm
(ready) Tj
1 0 0 1 284 273 Tm
108 Tz
(for) Tj
100 Tz
1 0 0 1 300 273 Tm
(an) Tj
1 0 0 1 313 273 Tm
107 Tz
(argument.) Tj
100 Tz
/F10 10 Tf
1 0 0 1 106 250 Tm
103 Tz
(Special) Tj
100 Tz
1 0 0 1 142 250 Tm
96 Tz
(Entry) Tj
100 Tz
1 0 0 1 171 250 Tm
(for) Tj
1 0 0 1 187 250 Tm
103 Tz
(PDE-BC) Tj
100 Tz
1 0 0 1 230 250 Tm
102 Tz
(Problems) Tj
100 Tz
/F9 10 Tf
1 0 0 1 131 235 Tm
109 Tz
(Another) Tj
100 Tz
1 0 0 1 171 235 Tm
109 Tz
(entry) Tj
100 Tz
1 0 0 1 198 235 Tm
105 Tz
(point) Tj
100 Tz
1 0 0 1 224 235 Tm
107 Tz
(can) Tj
100 Tz
1 0 0 1 243 235 Tm
(be) Tj
1 0 0 1 258 235 Tm
105 Tz
(made) Tj
100 Tz
1 0 0 1 286 235 Tm
(in) Tj
1 0 0 1 298 235 Tm
(POST) Tj
1 0 0 1 327 235 Tm
(to) Tj
1 0 0 1 340 235 Tm
106 Tz
(remove) Tj
100 Tz
1 0 0 1 377 235 Tm
(the) Tj
1 0 0 1 394 235 Tm
91 Tz
(01\)13) Tj
100 Tz
1 0 0 1 421 235 Tm
103 Tz
(variable) Tj
100 Tz
1 0 0 1 459 235 Tm
109 Tz
(parameters) Tj
100 Tz
1 0 0 1 511 235 Tm
105 Tz
(from) Tj
100 Tz
/F9 10 Tf
1 0 0 1 106 222 Tm
(the) Tj
1 0 0 1 124 222 Tm
(calls) Tj
1 0 0 1 148 222 Tm
(to) Tj
1 0 0 1 162 222 Tm
104 Tz
(Posts,) Tj
100 Tz
1 0 0 1 193 222 Tm
(AF,) Tj
1 0 0 1 215 222 Tm
67 Tz
(B) Tj
100 Tz
1 0 0 1 225 222 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 247 222 Tm
103 Tz
(Handle.) Tj
100 Tz
1 0 0 1 288 222 Tm
106 Tz
(This) Tj
100 Tz
1 0 0 1 312 222 Tm
(would) Tj
1 0 0 1 344 222 Tm
105 Tz
(make) Tj
100 Tz
1 0 0 1 372 222 Tm
(the) Tj
1 0 0 1 391 222 Tm
(use) Tj
1 0 0 1 410 222 Tm
111 Tz
(of) Tj
100 Tz
1 0 0 1 424 222 Tm
77 Tz
(1.~OST) Tj
100 Tz
1 0 0 1 454 222 Tm
(to) Tj
1 0 0 1 467 222 Tm
(solve) Tj
1 0 0 1 495 222 Tm
90 Tz
(P1\)13-BC) Tj
100 Tz
/F9 10 Tf
1 0 0 1 106 210 Tm
105 Tz
(problems) Tj
100 Tz
1 0 0 1 150 210 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 159 210 Tm
(little) Tj
1 0 0 1 182 210 Tm
104 Tz
(easier) Tj
100 Tz
1 0 0 1 212 210 Tm
(to) Tj
1 0 0 1 224 210 Tm
103 Tz
(explain) Tj
100 Tz
1 0 0 1 260 210 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 279 210 Tm
102 Tz
(accomplish.) Tj
100 Tz
1 0 0 1 337 210 Tm
105 Tz
(Once) Tj
100 Tz
1 0 0 1 365 210 Tm
(the) Tj
1 0 0 1 382 210 Tm
103 Tz
(package) Tj
100 Tz
1 0 0 1 420 210 Tm
(has) Tj
1 0 0 1 438 210 Tm
107 Tz
(firmed-up) Tj
100 Tz
1 0 0 1 485 210 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 494 210 Tm
92 Tz
(bit,) Tj
100 Tz
1 0 0 1 513 210 Tm
(such) Tj
/F9 10 Tf
1 0 0 1 106 198 Tm
(an) Tj
1 0 0 1 119 198 Tm
103 Tz
(overlay) Tj
100 Tz
1 0 0 1 154 198 Tm
93 Tz
(will) Tj
100 Tz
1 0 0 1 174 198 Tm
106 Tz
(undoubtedly) Tj
100 Tz
1 0 0 1 232 198 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 246 198 Tm
103 Tz
(provided.) Tj
100 Tz
/F10 10 Tf
1 0 0 1 106 174 Tm
96 Tz
(More) Tj
100 Tz
1 0 0 1 132 174 Tm
(General) Tj
1 0 0 1 172 174 Tm
95 Tz
(BC\202s) Tj
100 Tz
/F9 10 Tf
1 0 0 1 131 159 Tm
107 Tz
(Problems) Tj
100 Tz
1 0 0 1 176 159 Tm
104 Tz
(where) Tj
100 Tz
1 0 0 1 207 159 Tm
(the) Tj
1 0 0 1 225 159 Tm
(BC\202s) Tj
1 0 0 1 250 159 Tm
103 Tz
(involve) Tj
100 Tz
1 0 0 1 286 159 Tm
104 Tz
(giving) Tj
100 Tz
1 0 0 1 317 159 Tm
106 Tz
(both) Tj
100 Tz
1 0 0 1 341 159 Tm
80 Tz
(u) Tj
100 Tz
1 0 0 1 350 159 Tm
107 Tz
(and) Tj
100 Tz
/F10 8 Tf
1 0 0 1 370 159 Tm
(Ux) Tj
1 0 0 1 385 159 Tm
114 Tz
(at) Tj
100 Tz
/F9 10 Tf
1 0 0 1 397 159 Tm
108 Tz
(either) Tj
100 Tz
/F11 11 Tf
1 0 0 1 427 159 Tm
83 Tz
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1 0 0 1 249 692 Tm
(the) Tj
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104 Tz
(capabilities) Tj
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1 0 0 1 319 692 Tm
60 Tz
(oh~) Tj
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1 0 0 1 333 692 Tm
58 Tz
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(woLild) Tj
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1 0 0 1 394 692 Tm
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90 Tz
(n\(In\205lIIcal) Tj
100 Tz
1 0 0 1 493 692 Tm
117 Tz
(terms) Tj
100 Tz
1 0 0 1 522 692 Tm
86 Tz
(in) Tj
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(the) Tj
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96 Tz
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5 Ts

(2) Tj
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1 0 0 1 182 680 Tm
111 Tz
(This) Tj
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(allow) Tj
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98 Tz
(integro\205difierential) Tj
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1 0 0 1 353 680 Tm
107 Tz
(equations) Tj
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88 Tz
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94 Tz
(solved.) Tj
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97 Tz
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(such) Tj
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105 Tz
(problems) Tj
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1 0 0 1 172 668 Tm
107 Tz
(can) Tj
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1 0 0 1 192 668 Tm
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(currently) Tj
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1 0 0 1 236 668 Tm
(be) Tj
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104 Tz
(solved) Tj
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1 0 0 1 284 668 Tm
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(using) Tj
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(the) Tj
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91 Tz
(01\)13) Tj
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1 0 0 1 357 668 Tm
96 Tz
(facility) Tj
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(POST,) Tj
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105 Tz
(however,) Tj
100 Tz
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112 Tz
(cost) Tj
100 Tz
1 0 0 1 523 668 Tm
83 Tz
(Is) Tj
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(prohibitive.) Tj
100 Tz
1 0 0 1 160 654 Tm
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(it) Tj
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63 Tz
(right) Tj
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1 0 0 1 225 654 Tm
(would) Tj
1 0 0 1 256 654 Tm
107 Tz
(require) Tj
100 Tz
1 0 0 1 291 654 Tm
(that) Tj
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(the) Tj
1 0 0 1 329 654 Tm
(a) Tj
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(and) Tj
100 Tz
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77 Tz
(terms) Tj
100 Tz
1 0 0 1 394 654 Tm
58 Tz
(in) Tj
100 Tz
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(the) Tj
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83 Tz
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100 Tz
1 0 0 1 448 654 Tm
(also) Tj
1 0 0 1 470 654 Tm
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(have) Tj
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112 Tz
(parame) Tj
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(-) Tj
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67 Tz
(\() Tj
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1 0 0 1 135 644 Tm
120 Tz
(t,) Tj
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1 0 0 1 156 644 Tm
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(t\)) Tj
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/F10 5 Tf
1 0 0 1 165 644 Tm
160 Tz
(\),) Tj
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1 0 0 1 176 644 Tm
87 Tz
(seC) Tj
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1 0 0 1 196 644 Tm
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(\(5.4\).) Tj
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1 0 0 1 228 644 Tm
106 Tz
(The) Tj
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(BC\202s) Tj
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(and) Tj
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67 Tz
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100 Tz
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(have) Tj
100 Tz
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67 Tz
(such) Tj
100 Tz
1 0 0 1 382 644 Tm
72 Tz
(non-local) Tj
100 Tz
1 0 0 1 427 644 Tm
80 Tz
(terms) Tj
100 Tz
1 0 0 1 456 644 Tm
78 Tz
(and) Tj
100 Tz
1 0 0 1 477 644 Tm
33 Tz
(it) Tj
100 Tz
1 0 0 1 488 644 Tm
83 Tz
(would) Tj
100 Tz
1 0 0 1 520 644 Tm
67 Tz
(he) Tj
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1 0 0 1 103 632 Tm
105 Tz
(mathematically) Tj
100 Tz
1 0 0 1 174 632 Tm
104 Tz
(pretty) Tj
100 Tz
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1 0 0 1 205 632 Tm
(if) Tj
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(the) Tj
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(AF) Tj
1 0 0 1 255 632 Tm
105 Tz
(term) Tj
100 Tz
1 0 0 1 280 632 Tm
104 Tz
(could) Tj
100 Tz
1 0 0 1 309 632 Tm
(also.) Tj
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(I) Tj
100 Tz
1 0 0 1 342 632 Tm
106 Tz
(lowever,) Tj
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92 Tz
(the) Tj
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95 Tz
(Jacobian) Tj
100 Tz
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94 Tz
(matrix,) Tj
100 Tz
1 0 0 1 485 632 Tm
94 Tz
(instead) Tj
100 Tz
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100 Tz
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73 Tz
(being) Tj
100 Tz
1 0 0 1 130 621 Tm
79 Tz
(banded,) Tj
100 Tz
1 0 0 1 168 621 Tm
83 Tz
(would) Tj
100 Tz
1 0 0 1 198 621 Tm
67 Tz
(be) Tj
100 Tz
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54 Tz
(full) Tj
100 Tz
1 0 0 1 230 621 Tm
83 Tz
(and) Tj
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/F9 10 Tf
1 0 0 1 250 621 Tm
108 Tz
(dense) Tj
100 Tz
1 0 0 1 278 621 Tm
(in) Tj
1 0 0 1 290 621 Tm
106 Tz
(general.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 331 621 Tm
75 Tz
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1 0 0 1 354 621 Tm
83 Tz
(would) Tj
100 Tz
1 0 0 1 384 621 Tm
64 Tz
(significantly) Tj
100 Tz
/F9 11 Tf
1 0 0 1 439 621 Tm
92 Tz
(increase) Tj
100 Tz
1 0 0 1 478 621 Tm
92 Tz
(the) Tj
100 Tz
1 0 0 1 495 621 Tm
97 Tz
(running) Tj
100 Tz
/F1 10 Tf
1 0 0 1 103 608 Tm
75 Tz
(time) Tj
100 Tz
1 0 0 1 127 608 Tm
61 Tz
(for) Tj
100 Tz
1 0 0 1 144 608 Tm
79 Tz
(such) Tj
100 Tz
1 0 0 1 169 608 Tm
78 Tz
(problems,) Tj
100 Tz
1 0 0 1 217 608 Tm
67 Tz
(but) Tj
100 Tz
1 0 0 1 235 608 Tm
67 Tz
(also) Tj
100 Tz
/F9 10 Tf
1 0 0 1 257 608 Tm
(allow) Tj
1 0 0 1 284 608 Tm
106 Tz
(solution) Tj
100 Tz
1 0 0 1 324 608 Tm
(of) Tj
1 0 0 1 338 608 Tm
75 Tz
(a) Tj
100 Tz
1 0 0 1 347 608 Tm
91 Tz
(much) Tj
100 Tz
1 0 0 1 376 608 Tm
106 Tz
(broader) Tj
100 Tz
1 0 0 1 414 608 Tm
(range) Tj
1 0 0 1 442 608 Tm
(of) Tj
1 0 0 1 456 608 Tm
105 Tz
(problems.) Tj
100 Tz
1 0 0 1 508 608 Tm
119 Tz
(Non) Tj
100 Tz
(-) Tj
1 0 0 1 103 597 Tm
95 Tz
(local) Tj
100 Tz
/F1 10 Tf
1 0 0 1 126 597 Tm
105 Tz
(PDE) Tj
100 Tz
1 0 0 1 151 597 Tm
80 Tz
(terms) Tj
100 Tz
1 0 0 1 180 597 Tm
78 Tz
(can) Tj
100 Tz
/F9 10 Tf
1 0 0 1 199 597 Tm
(be) Tj
1 0 0 1 213 597 Tm
108 Tz
(added) Tj
100 Tz
1 0 0 1 243 597 Tm
(fairly) Tj
1 0 0 1 269 597 Tm
(easily) Tj
1 0 0 1 298 597 Tm
(to) Tj
1 0 0 1 311 597 Tm
104 Tz
(POST,) Tj
100 Tz
1 0 0 1 344 597 Tm
108 Tz
(but) Tj
100 Tz
1 0 0 1 362 597 Tm
105 Tz
(their) Tj
100 Tz
1 0 0 1 387 597 Tm
107 Tz
(implementation) Tj
100 Tz
1 0 0 1 459 597 Tm
(awaits) Tj
1 0 0 1 490 597 Tm
105 Tz
(sufficient) Tj
100 Tz
/F9 10 Tf
1 0 0 1 103 585 Tm
106 Tz
(user) Tj
100 Tz
1 0 0 1 124 585 Tm
106 Tz
(demand.) Tj
100 Tz
/F10 10 Tf
1 0 0 1 102 561 Tm
(Other) Tj
1 0 0 1 131 561 Tm
103 Tz
(Spatial) Tj
100 Tz
1 0 0 1 167 561 Tm
105 Tz
(Discretization) Tj
100 Tz
1 0 0 1 234 561 Tm
104 Tz
(Techniques) Tj
100 Tz
/F9 10 Tf
1 0 0 1 127 546 Tm
103 Tz
(B-splines) Tj
100 Tz
1 0 0 1 171 546 Tm
(are) Tj
1 0 0 1 190 546 Tm
105 Tz
(used) Tj
100 Tz
1 0 0 1 216 546 Tm
(in) Tj
1 0 0 1 230 546 Tm
(the) Tj
1 0 0 1 249 546 Tm
110 Tz
(current) Tj
100 Tz
1 0 0 1 287 546 Tm
107 Tz
(implementation) Tj
100 Tz
1 0 0 1 361 546 Tm
107 Tz
(due) Tj
100 Tz
1 0 0 1 382 546 Tm
(to) Tj
1 0 0 1 397 546 Tm
(their) Tj
1 0 0 1 421 546 Tm
105 Tz
(excellent) Tj
100 Tz
/F9 9 Tf
1 0 0 1 466 546 Tm
111 Tz
(approximatlOfl) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 533 Tm
107 Tz
(properties) Tj
100 Tz
1 0 0 1 150 533 Tm
(\(see) Tj
1 0 0 1 171 533 Tm
105 Tz
(Appendix) Tj
100 Tz
1 0 0 1 218 533 Tm
33 Tz
(I) Tj
100 Tz
1 0 0 1 223 533 Tm
33 Tz
(\)) Tj
100 Tz
1 0 0 1 230 533 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 250 533 Tm
(the) Tj
1 0 0 1 267 533 Tm
(fact) Tj
1 0 0 1 287 533 Tm
(that) Tj
1 0 0 1 308 533 Tm
110 Tz
(there) Tj
100 Tz
1 0 0 1 334 533 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 344 533 Tm
75 Tz
(a) Tj
100 Tz
/F3 10 Tf
1 0 0 1 352 533 Tm
63 Tz
(local) Tj
100 Tz
/F9 10 Tf
1 0 0 1 375 533 Tm
(basis) Tj
/F1 10 Tf
1 0 0 1 399 533 Tm
61 Tz
(for) Tj
100 Tz
1 0 0 1 416 533 Tm
88 Tz
(them) Tj
100 Tz
1 0 0 1 442 533 Tm
80 Tz
(which) Tj
100 Tz
/F10 8 Tf
1 0 0 1 471 533 Tm
50 Tz
(y) Tj
100 Tz
/F9 9 Tf
1 0 0 1 479 533 Tm
112 Tz
(elds) Tj
100 Tz
/F3 10 Tf
1 0 0 1 500 533 Tm
81 Tz
(banded) Tj
100 Tz
/F9 10 Tf
1 0 0 1 102 521 Tm
102 Tz
(Jacobians.) Tj
100 Tz
1 0 0 1 153 521 Tm
111 Tz
(This) Tj
100 Tz
1 0 0 1 176 521 Tm
(choice) Tj
1 0 0 1 209 521 Tm
83 Tz
(is) Tj
100 Tz
1 0 0 1 220 521 Tm
105 Tz
(made) Tj
100 Tz
1 0 0 1 248 521 Tm
(for) Tj
1 0 0 1 264 521 Tm
106 Tz
(general) Tj
100 Tz
1 0 0 1 300 521 Tm
108 Tz
(robustness,) Tj
100 Tz
1 0 0 1 354 521 Tm
103 Tz
(reliability) Tj
100 Tz
1 0 0 1 399 521 Tm
88 Tz
(an.d) Tj
100 Tz
1 0 0 1 418 521 Tm
(efficiency.) Tj
1 0 0 1 470 521 Tm
33 Tz
(I) Tj
100 Tz
1 0 0 1 475 521 Tm
111 Tz
(lowe\\er.) Tj
100 Tz
1 0 0 1 517 521 Tm
91 Tz
(for) Tj
100 Tz
1 0 0 1 102 509 Tm
105 Tz
(particular) Tj
100 Tz
1 0 0 1 147 509 Tm
105 Tz
(problems) Tj
100 Tz
1 0 0 1 192 509 Tm
110 Tz
(there) Tj
100 Tz
1 0 0 1 219 509 Tm
94 Tz
(may) Tj
100 Tz
1 0 0 1 241 509 Tm
(be) Tj
1 0 0 1 255 509 Tm
109 Tz
(other) Tj
100 Tz
1 0 0 1 283 509 Tm
104 Tz
(\(non-local\)) Tj
100 Tz
1 0 0 1 336 509 Tm
106 Tz
(approximation) Tj
100 Tz
1 0 0 1 403 509 Tm
(spaces) Tj
1 0 0 1 435 509 Tm
104 Tz
(which,) Tj
100 Tz
1 0 0 1 467 509 Tm
105 Tz
(although) Tj
100 Tz
1 0 0 1 511 509 Tm
94 Tz
(they) Tj
100 Tz
/F1 10 Tf
1 0 0 1 102 497 Tm
63 Tz
(yield) Tj
100 Tz
/F9 10 Tf
1 0 0 1 127 497 Tm
108 Tz
(dense) Tj
100 Tz
1 0 0 1 158 497 Tm
105 Tz
(matrices,) Tj
100 Tz
1 0 0 1 202 497 Tm
(are) Tj
1 0 0 1 221 497 Tm
(very) Tj
1 0 0 1 244 497 Tm
103 Tz
(efficient) Tj
100 Tz
1 0 0 1 284 497 Tm
106 Tz
(because) Tj
100 Tz
1 0 0 1 324 497 Tm
(very) Tj
1 0 0 1 347 497 Tm
(few) Tj
1 0 0 1 368 497 Tm
(basis) Tj
1 0 0 1 394 497 Tm
105 Tz
(functions) Tj
100 Tz
1 0 0 1 439 497 Tm
(are) Tj
1 0 0 1 457 497 Tm
107 Tz
(needed) Tj
100 Tz
1 0 0 1 493 497 Tm
(to) Tj
/F9 9 Tf
1 0 0 1 507 497 Tm
120 Tz
(accu) Tj
100 Tz
(-) Tj
/F9 11 Tf
1 0 0 1 102 485 Tm
88 Tz
(rately) Tj
100 Tz
1 0 0 1 129 485 Tm
98 Tz
(approximate) Tj
100 Tz
1 0 0 1 188 485 Tm
92 Tz
(the) Tj
100 Tz
1 0 0 1 205 485 Tm
97 Tz
(solution.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 250 485 Tm
42 Tz
(It) Tj
100 Tz
1 0 0 1 260 485 Tm
42 Tz
(is) Tj
100 Tz
1 0 0 1 270 485 Tm
76 Tz
(conceivable) Tj
100 Tz
1 0 0 1 325 485 Tm
63 Tz
(that) Tj
100 Tz
1 0 0 1 345 485 Tm
50 Tz
(a) Tj
100 Tz
1 0 0 1 353 485 Tm
79 Tz
(package) Tj
100 Tz
1 0 0 1 391 485 Tm
73 Tz
(allowing) Tj
100 Tz
1 0 0 1 431 485 Tm
67 Tz
(the) Tj
100 Tz
1 0 0 1 448 485 Tm
71 Tz
(user) Tj
100 Tz
1 0 0 1 470 485 Tm
58 Tz
(to) Tj
100 Tz
1 0 0 1 482 485 Tm
64 Tz
(specif~) Tj
100 Tz
/F9 10 Tf
1 0 0 1 515 485 Tm
(the) Tj
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1 0 0 1 102 473 Tm
(basis) Tj
1 0 0 1 126 473 Tm
107 Tz
(functions,) Tj
100 Tz
1 0 0 1 173 473 Tm
107 Tz
(and) Tj
100 Tz
1 0 0 1 193 473 Tm
(the) Tj
1 0 0 1 210 473 Tm
94 Tz
(way) Tj
100 Tz
1 0 0 1 230 473 Tm
(to) Tj
1 0 0 1 242 473 Tm
108 Tz
(compute) Tj
100 Tz
1 0 0 1 284 473 Tm
(the) Tj
1 0 0 1 300 473 Tm
111 Tz
(\(jalerkin) Tj
100 Tz
1 0 0 1 342 473 Tm
108 Tz
(integrals,) Tj
100 Tz
1 0 0 1 386 473 Tm
104 Tz
(could) Tj
100 Tz
1 0 0 1 414 473 Tm
89 Tz
(be) Tj
100 Tz
1 0 0 1 427 473 Tm
110 Tz
(created) Tj
100 Tz
1 0 0 1 462 473 Tm
(and) Tj
1 0 0 1 481 473 Tm
110 Tz
(even) Tj
100 Tz
1 0 0 1 506 473 Tm
(made) Tj
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60 Tz
(efficient.) Tj
100 Tz
1 0 0 1 146 461 Tm
83 Tz
(Such) Tj
100 Tz
1 0 0 1 171 461 Tm
50 Tz
(a) Tj
100 Tz
1 0 0 1 179 461 Tm
67 Tz
(project) Tj
100 Tz
1 0 0 1 211 461 Tm
69 Tz
(awaits) Tj
100 Tz
1 0 0 1 241 461 Tm
65 Tz
(sufficient) Tj
100 Tz
1 0 0 1 285 461 Tm
71 Tz
(user) Tj
100 Tz
1 0 0 1 306 461 Tm
86 Tz
(demand.) Tj
100 Tz
/F10 10 Tf
1 0 0 1 102 437 Tm
97 Tz
(Banded) Tj
100 Tz
1 0 0 1 139 437 Tm
(PDE) Tj
1 0 0 1 163 437 Tm
106 Tz
(Systems) Tj
100 Tz
/F1 10 Tf
1 0 0 1 126 422 Tm
83 Tz
(There) Tj
100 Tz
1 0 0 1 158 422 Tm
67 Tz
(are) Tj
100 Tz
1 0 0 1 176 422 Tm
68 Tz
(situations) Tj
100 Tz
1 0 0 1 224 422 Tm
83 Tz
(where) Tj
100 Tz
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67 Tz
(the) Tj
100 Tz
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64 Tz
(P1\)13\202s) Tj
100 Tz
1 0 0 1 309 422 Tm
80 Tz
(themselves) Tj
100 Tz
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67 Tz
(are) Tj
100 Tz
1 0 0 1 383 422 Tm
79 Tz
(banded,) Tj
100 Tz
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63 Tz
(that) Tj
100 Tz
1 0 0 1 445 422 Tm
44 Tz
(is,) Tj
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75 Tz
(a,) Tj
100 Tz
/F9 9 Tf
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114 Tz
(and) Tj
100 Tz
/F11 12 Tf
1 0 0 1 495 422 Tm
140 Tz
(I) Tj
100 Tz
/F9 10 Tf
1 0 0 1 510 422 Tm
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(ink) Tj
100 Tz
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83 Tz
(depend) Tj
100 Tz
1 0 0 1 137 409 Tm
83 Tz
(on) Tj
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58 Tz
(u) Tj
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(1) Tj
100 Tz
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-5 Ts
(for) Tj
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1 0 0 1 182 409 Tm
125 Tz
(j) Tj
100 Tz
/F9 10 Tf
1 0 0 1 191 409 Tm
96 Tz
(\203near\204) Tj
100 Tz
/F11 10 Tf
1 0 0 1 222 409 Tm
80 Tz
(i.) Tj
100 Tz
/F1 10 Tf
1 0 0 1 236 409 Tm
83 Tz
(Advantage) Tj
100 Tz
1 0 0 1 286 409 Tm
78 Tz
(can) Tj
100 Tz
1 0 0 1 306 409 Tm
75 Tz
(be) Tj
100 Tz
1 0 0 1 320 409 Tm
73 Tz
(taken) Tj
100 Tz
1 0 0 1 348 409 Tm
75 Tz
(of) Tj
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58 Tz
(this) Tj
100 Tz
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70 Tz
(structure) Tj
100 Tz
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58 Tz
(to) Tj
100 Tz
1 0 0 1 436 409 Tm
75 Tz
(decrease) Tj
100 Tz
1 0 0 1 478 409 Tm
67 Tz
(the) Tj
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89 Tz
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