Numerical Methods for Ordinary Dierential Equations Episode 6 ppsx
Numerical Methods for Ordinary Dierential Equations Episode 6 ppsx
... c 3 c 6 + c 4 c 6 12 − c 3 c 4 c 6 6 , (326b) 7 i=1 b i (1 − c i )(c i − c 6 )(c i −c 4 )c i = 1 20 − c 4 + c 6 12 + c 4 c 6 6 , (326c) 7 i=1 b i (1 − c i )(c i − c 6 )c i = 1 12 − c 6 6 , (326d) 162 ... manner: 0 1 4 1 4 1 4 1 8 1 8 1 2 00 1 2 3 4 3 16 − 3 8 3 8 9 16 1 − 3 7 8 7 6 7 − 12 7 8 7 7 90 0 16 45 2 15 16 45 7 90 . 166 NUMERICAL METHODS FOR ORD...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 8 ppsx
... + 1 9 z 2 − 1 72 z 3 + 1 1008 z 4 − 1 30240 z 5 6 1+ 1 2 z + 5 44 z 2 + 1 66 z 3 + 1 792 z 4 + 1 15840 z 5 + 1 66 5280 z 6 1 − 1 2 z + 5 44 z 2 − 1 66 z 3 + 1 792 z 4 − 1 15840 z 5 + 1 66 5280 z 6 7 1+ 1 2 z + 3 26 z 2 + 5 312 z 3 + 5 3432 z 4 + 1 11440 z 5 + 1 308880 z 6 + 1 17297280 z 7 1 ... + 3 22 z 2 − 2 99 z 3 + 1 528 z 4 − 1 9240 z 5 + 1 33 264 0 z 6 7 1+ 6 13 z + 5...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 9 ppsx
... polynomial 1859 76 12 − 1490400λ 11 + 460 1448λ 10 − 7257 168 λ 9 + 68 42853λ 8 −4181 760 λ 7 +17242 56 6 −4872 96 5 +941 76 4 −12192λ 3 +1008λ 2 −48λ+1. 37 Symplectic Runge–Kutta Methods 370 Maintaining quadratic ... −b s 280 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 38 Algebraic Properties of Runge–Kutta Methods 380 Motivation For any specific N-dimensional...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 1 docx
... T 0 ◦ 6. 2831853072 3 ◦ 6. 284 262 0831 6 ◦ 6. 2874944421 9 ◦ 6. 2928884880 12 ◦ 6. 3004544311 15 ◦ 6. 3102 066 431 18 ◦ 6. 322 163 73 56 21 ◦ 6. 3 363 4 866 30 24 ◦ 6. 3527888501 27 ◦ 6. 3715 163 462 30 ◦ 6. 392 568 0085 where q = ... considerations 366 461 Representation of data 367 462 Variable stepsize for Nordsieck methods 371 463 Local error estimation 372 5 Gene...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 2 docx
... were (y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 6 )=(0.994, 0, 0, 0, −2.0015851 063 790825224, 0) and the period was 17. 065 2 165 60157 96. 34 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS y 1 y 2 Figure 122(i) Solution to problem ... −4a 2 (a 1 − a 2 ) −8a 3 (a 2 − a 3 ) −··· . 18 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 02 46 u 02 468 v Figure 1 06( i) Phas...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 3 pot
... 2 561 78.9889×10 −10 4.1893 80 61 150. 262 6×10 −10 4.0904 160 14949 .61 76 10 −10 4.0442 320 369 6.5 967 ×10 −10 4.0218 64 0 919.1 362 ×10 −10 4.0108 1280 229. 162 9×10 −10 4.0054 2 560 57.2134×10 −10 4.00 26 5120 ... 0.000014 16 −0.00003945 n y 3 error Ratio y 4 error Ratio 32 0.0403 863 6 −0.01548159 3.9497 4.1552 64 0.01022525 −0.00372585 4.0132 4. 065 9 128 0.00254793 −0.0009 163 6...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 4 doc
... 1 1 2 1 1 2 1 2 − 1 12 2 5 12 2 3 − 1 12 1 24 3 3 8 19 24 − 5 24 1 24 − 19 720 4 251 720 323 360 − 11 30 53 360 − 19 720 3 160 5 95 288 1427 1440 − 133 240 241 720 − 173 1440 3 160 − 863 60 480 6 19087 60 480 2713 2520 − 15487 20 160 5 86 945 − 67 37 20 160 263 2520 − 863 60 480 275 24192 7 5257 17280 139849 120 960 − 4511 4480 123133 120 960 − 88547 120 960 1537 4480...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 5 docx
... 10 −2 3.988 76 10 8 −4 2.339 86 × 10 −2 3.54007 13 8 −5 4.95205 × 10 −3 4.72504 19 8 6 1.0 465 5 × 10 −3 4.73180 30 8 −7 2.2 468 4 × 10 −4 4 .65 7 86 50 8 −8 4.8 966 3 × 10 −5 4.58854 82 8 −9 1.02 365 × 10 −5 4.78350 137 8 −10 2.15123 ... labelled by Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher © 2008 John Wiley & Sons, Ltd. ISBN: 978-...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 7 potx
... IIA (s =3,p=5), 4− √ 6 10 88−7 √ 6 360 2 96 169 √ 6 1800 −2+3 √ 6 225 4+ √ 6 10 2 96+ 169 √ 6 1800 88+7 √ 6 360 −2−3 √ 6 225 1 16 √ 6 36 16+ √ 6 36 1 9 16 √ 6 36 16+ √ 6 36 1 9 Lobatto III (s ... 0 6 √ 6 10 9+ √ 6 75 24+ √ 6 120 168 −73 √ 6 600 6+ √ 6 10 9− √ 6 75 168 +73 √ 6 600 24− √ 6 120 1 9 16+ √ 6 36 16 √ 6 36 Radau IA...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 10 pot
... 1 1 2 1 2 0 1 2 1 2 1 3 1 3 0 1 3 1 3 1 6 1 6 1 72 11 72 11+r 3 72 1 4 1 4 1 108 13 54 26+ r 4 108 1 8 5 36 1 2 16 13 108 26+ 3r 3 +r 4 2 16 1 12 1 9 − 1 2 16 19 2 16 19+6r 3 −r 4 2 16 1 24 1 24 0 1 36 2+r 3 72 We do not ... requirements. Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher © 2008 John Wiley & Sons, Ltd. ISBN: 978-0-...
Ngày tải lên: 13/08/2014, 05:21