Finite Differences - . . ‘/5 SUM/Hag a...

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L’KAIMP’es wf’n? dome USWj 0.05 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.? 0.?5 0.8 0.85 0.9 0.95 1.05 1.1 1.15 1.2 0.15 0.15 0.3 0.45 0.6 0.?5 0.9 1.05 1.2 1.35 1.5 1.65 1.8 1.95 2.1 2.25 2.4 2.55 2.? 2.85 3.15 3.3 3.45 3.6 /‘ Ax = 0.05 (z Step Explicit 1 1.05 1.1025 1.15?625 1.21550625 1.2?62815 63 1.340095 641 1.40?100423 1.4??455444 1.55 13 28216 1.62889462? 1.?103 39 358 1.79585 63 26 1.885 649 142 1.9 ?99 3 1599 2.0?89 281?9 2.1828?4588 2.29 20183 18 2.406619 234 2.5 26950195 2.65 3 29 ??05 2. ?859 6259 2.925260?2 3 .0?15 23 ?5 6 3.225099944 <2 Step Explicit 1 1.15 1.3225 1.5 208?5 1. ?4900625 2.01135 ?188 2.313060?66 2.66001988 3.059022863 3.51?8?6292 4.04555 ??36 4.65 239 139 6 5.350250105 6.152?8?621 ?.0?5 ?05 ?64 8.13 ?061629 9.35 ?6208?4 10.?61264 12. 3 ?545 3 61 14.231??165 16. 3 665 3 ?39 18.821518 21.644?45? 24.89 145 ?5 6 28.6251?619 Implicit 1 1.05 2631579 1.108033241 1.166350?8 1.22??3 ?663 1.29 2355435 1.3603 ?4142 1.4319?2?81 1.50?3 39 ?? 1.5866?3442 1.6?01825? 1.?58086916 1.85061?806 1.948018?43 2050546046 2158469522 2.2?20?3181 2.39165598 2.5 1?5 3 261 2.65003432? 2.?89509818 2.9 3 63 26124 3.090869604 3.253546951 3.424?86265 Implicit 1 1.1?64?0588 1.384083045 1.628332994 1.9156858?5 2.253?48089 2.65146834 3.1193?451? 3.66985 23?3 4.31?4?3 38 5.0?9 38044? 5.9 ?5 ?41?03 ?.030284356 8.2?09 22??2 9.?3049 ?3?9 11.44?64398 13.46?81644 15.84448993 18.6405 ?639 21.9 300898? 25.800105?3 30.35 306556 35.?094889 42.01116341 49.42489813 Exact 1 1.0512?1096 1.1051?0918 1.161834243 1.221402?58 1.28402541? 1.349858808 1.419067549 1.491824698 1.568312185 1.648?212?1 1. ?33 25 3018 1.8221188 1.915540829 2.013 ?5 2?0? 2.11?00001? 2.2255409 28 2. 3 39 64685 2 2.459 603 111 2.585 ?09 659 2.?18281828 2.85?651118 3.004166024 3.15819291 3.3201169 23 Exact 1 1.161834243 1.349858808 1.568312185 1.8221188 2.11?00001? 2.459603111 2.85?651118 3.3201169 23 3.85?425531 4.4816890? 5.2069 ?982? 6.049 64?464 ?.028687581 8.166169913 9.48??35836 11.02317638 12.80?103 ?8 14.8?9?31?2 1?.28??8184 20.0855 3 69 2 23.33606458 2?.11263892 4/5 3.5 2.5 —o—Explicit -I-lmp|icit fl-EXEICT 1.5 Ody 1 slowly X As “Hat S'l'ep $13e jets (Mfr, 'l‘Le Cl/V‘OV‘ 5195 (auger, loud‘ sh“ grows ymafwclly 50 _—— -I-|mp|icit 1.318131: “5 30 20 0 I D 0.5 1 1.5 2 2.5 3 3.5 4 X 3 1.50039 23 1 36.59823444 0.3 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.? 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5.4 5.? 6.3 6.6 6.9 7.2 5/5 Whén Step 3136 391-5 172; 14-qu Hie error- AX :03 in 'Hflfl CK’PKCH— (firwa Ji-W'mncg) grows Cloi'aklj. 7W5 is divergence. <= Step Explicit Implicit Exact 6000 1 1 1 1.3 1.423511423 1.343353303 1.63 2.0403163 21 1.3221133 * EXDIiCi 2.131 2.315451335 2.453603111 50”” ____ _._|mpliciT 2.3561 4.164331213 3.320116323 3.11233 5.343301321 4.43163301 'F Exam 4.326303 3.433353152 6.043641464 4000 6.2143511 12.14265613 3.166163313 3.15130121 11.34665256 11.02311633 10.60443331 24.13033222 14.31313112 _ 13.13534313 35.40133115 20.03553632 “if- 3000 11.32160334 50.51333101 21.11263332 23.23303512 12.24161531 36.53323444 30.23151066 103.2103131 43.40244311 2m 33.31316336 141.4441133 66.63633104 51.13533301 210.6344434 30.0111313 66.54166032 300.3063543 121.5104115 36.50415313 423.3662213 164.0213013 1m 112.455401 614.0346013 221.4064162 146.132023 311.2130026 233.361401 130.0436311 1253.254233 403.4231335 ' ‘ __ 24?. 544-5 U _-"'I. _-"'I. .I"'-_ 3". .""'. -"'I 1"“ -"~'- I'III'I "fll'l "I' "I' 'I' I I 321.1333313 2551.661315 135.0351332 U 3 3 4 5 5 T 3 411.5330541 3653.302533 332.2141156 x 542.3001104 5213.11133 1333.430164 “C fine I». 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This note was uploaded on 02/21/2012 for the course MET 581 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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Finite Differences - . . ‘/5 SUM/Hag a...

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