Numerical Methods for Ordinary Dierential Equations Episode 7 potx

... − 1 2 3 4 − 93 22 0 24921 1408 − 10059 70 4 73 5 1408 73 5 70 4 17 19 865 473 13055 10295610642 0 − 9 670 70 67 28 670 62 15526951598 571 978 869 279 49088 8 171 12 67 − 452648800 245133801 270 189568 4 679 8 271 1 1 98 76 5 00 − 9 83 1 071 1600 − 11 75 64 225 390963 22 576 00 188 3315 00 1593 75 53 2943 20800 1 97 975 576 2 275 2 476 099 29348800 2 39 − 142 1989 00 2412...

Ngày tải lên: 13/08/2014, 05:21

... methods 373 501 Transformations of methods 375 502 Runge–Kutta methods as general linear methods 376 503 Linear multistep methods as general linear methods 377 504 Some known unconventional methods ... 3 67 462 Variable stepsize for Nordsieck methods 371 463 Local error estimation 372 5 General Linear Methods 373 50 Representing Methods in General Linear Form 373...

Ngày tải lên: 13/08/2014, 05:21

... these assumptions, the equations of motion become 38 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 13 Difference Equation Problems 130 Introduction to difference equations While differential equations ... were (y 1 ,y 2 ,y 3 ,y 4 ,y 5 ,y 6 )=(0.994, 0, 0, 0, −2.001585106 379 0825224, 0) and the period was 17. 0652165601 579 6. 34 NUMERICAL METHODS FOR ORDINARY DIF...

Ngày tải lên: 13/08/2014, 05:21

... three stepsizes we have used, the errors are respectively 1 .72 474 5 − 1.6 875 55 = 0.0 371 90, 1 .72 474 5 − 1 .70 6 570 = 0.018 175 and 1 .72 474 5 −1 .71 576 0 = 0.008985. These error values approximately drop by ... 0.018 174 89 −0.0 173 7 078 47 20 0.00898483 −0.00 878 393 80 40 0.0044 670 4 −0.00441680 149 80 0.0022 272 1 −0.00221462 240 160 0.00111203 −0.00110889 480 320 0.00055562 −...

Ngày tải lên: 13/08/2014, 05:21

... − 1 2 2 3 2 − 1 2 5 12 3 23 12 − 4 3 5 12 − 3 8 4 55 24 − 59 24 37 24 − 3 8 251 72 0 5 1901 72 0 − 13 87 360 109 30 − 6 37 360 251 72 0 − 95 288 6 4 277 1440 − 2641 480 4991 72 0 − 3649 72 0 959 480 − 95 288 190 87 60480 7 19 872 1 60480 − 186 37 2520 235183 20160 − 1 075 4 945 13 571 3 20160 − 5603 2520 190 87 60480 − 52 57 172 80 8 16083 4480 − 1152169 120960 242653 13440 −...

Ngày tải lên: 13/08/2014, 05:21

... 10 −5 4 .78 350 1 37 8 −10 2.15123 × 10 −6 4 .75 845 228 8 −11 4.53436 × 10 7 4 .74 429 382 8 −12 9. 575 67 × 10 −8 4 .73 529 642 8 −13 2.01165 × 10 −8 4 .76 011 1 078 8 −14 4.22848 × 10 −9 4 .75 7 37 1810 committed ... labelled by Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher © 2008 John Wiley & Sons, Ltd. ISBN: 978 -0- 470 -72 335 -7...

Ngày tải lên: 13/08/2014, 05:21

... 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 ORDINARY DIFFERENTIAL EQUATIONS Another approach would be to assume ... = 1 p! . (324h) 170 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS 32 Low Order Explicit Methods 320 Methods of orders less than 4...

Ngày tải lên: 13/08/2014, 05:21

... + 3 22 z 2 − 2 99 z 3 + 1 528 z 4 − 1 9240 z 5 + 1 332640 z 6 7 1+ 6 13 z + 5 52 z 2 + 5 429 z 3 + 1 1144 z 4 + 1 2 574 0 z 5 + 1 1235520 z 6 1 − 7 13 z + 7 52 z 2 − 35 171 6 z 3 + 7 3432 z 4 − 7 51480 z 5 + 7 1235520 z 6 − 1 8648640 z 7 For convenience, ... y n and y n−1 from (357f) and (357g) and rearrange to deduce (357e).  234 NUMERICAL METHODS FOR ORDINARY DIFFE...

Ngày tải lên: 13/08/2014, 05:21

... 4601448λ 10 − 72 571 68λ 9 + 6842853λ 8 −418 176 0λ 7 + 172 4256λ 6 −4 872 96λ 5 +94 176 λ 4 −12192λ 3 +1008λ 2 −48λ+1. 37 Symplectic Runge–Kutta Methods 370 Maintaining quadratic invariants We recall Definition 357B ... + 15 2 ξ 2 − 10 3 ξ 3 + 5 8 ξ 4 − 1 20 ξ 5 + 1 72 0 ξ 6 71 − 7 + 21 2 ξ 2 − 35 6 ξ 3 + 35 24 ξ 4 − 7 40 ξ 5 + 7 720 ξ 6 − 1 5040 ξ 7 81− 8ξ +14ξ 2 − 28 3 ξ 3 +...

Ngày tải lên: 13/08/2014, 05:21

... requirements. Numerical Methods for Ordinary Differential Equations, Second Edition. J. C. Butcher © 2008 John Wiley & Sons, Ltd. ISBN: 978 -0- 470 -72 335 -7 332 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL ... 1) 3 + 251 72 0 (z − 1) 4 − 95 288 (z − 1) 5 + 190 87 60480 (z − 1) 6 − 52 57 172 80 (z −1) 7 + 1 070 0 17 3628800 (z − 1) 8 − 2 571 3 89600 (z − 1) 9 + 268...

Ngày tải lên: 13/08/2014, 05:21