Tài liệu Integration of Ordinary Differential Equations part 3 doc

... a i b ij c i c ∗ i 1 37 37 8 2825 27648 2 1 5 1 5 0 0 3 3 10 3 40 9 40 250 621 18575 4 838 4 4 3 5 3 10 − 9 10 6 5 125 594 135 25 55296 5 1 − 11 54 5 2 − 70 27 35 27 0 277 1 433 6 6 7 8 1 631 55296 175 512 575 138 24 44275 110592 2 53 4096 512 1771 1 4 j ... = -0.9,b 43= 1.2, b51 = -11.0/54.0, b52=2.5,b 53 = -70.0/27.0,b54 =35 .0/27.0, b61=1 631 .0/55296.0,b62=175.0/512.0,b 6...

Ngày tải lên: 24/12/2013, 12:16

... odeint are drivers. Section 16.6 of this chapter treats the subject of stiff equations, relevant both to ordinary differential equations and also to partial differential equations (Chapter 19). ... auxiliary variables. The generic problem in ordinary differential equations is thus reduced to the study of a set of N coupled first-order differential equations for th...

Ngày tải lên: 15/12/2013, 04:15

... 7. Lambert, J. 19 73, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: ... 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyri...

Ngày tải lên: 15/12/2013, 04:15

... 722 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) 1988-1992 ... ,n−1 y(x+H)≈y n ≡ 1 2 [z n +z n−1 +hf(x + H, z n )] (16 .3. 2) 16 .3 Modified Midpoint Method 7 23 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5...

Ngày tải lên: 24/12/2013, 12:16

... Converged. exitflag=1; break; } 730 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) ... quite a large 726 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-52...

Ngày tải lên: 24/12/2013, 12:16

... 732 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Copyright (C) ... 505– 535 . [3] 16.5 Second-Order Conservative Equations Usually when you have a system of high-order differential equations to solve it is best to reformulate them as a system of first-order equ...

Ngày tải lên: 24/12/2013, 12:16

... 6.02015272865 #define C32 0.1597506846 73 #define C41 -1.85 634 3618677 #define C42 -8.50 538 085819 #define C 43 -2.084075 136 02 #define B1 3. 9575 037 46 63 #define B2 4.62489 238 836 #define B3 0.6174772 638 73 #define ... those of Shampine simply by replacing the #define statements: #define GAM 0. 231 #define A21 2.0 #define A31 4.52470820 736 #define A32 4.1 635 2878860 #defin...

Ngày tải lên: 24/12/2013, 12:16

... Mathematical Software , vol. 8, pp. 93 1 13. [3] Enright, W.H., and Pryce, J.D. 1987, ACM Transactions on Mathematical Software , vol. 13, pp. 1–27. [4] Bader, G., and Deuflhard, P. 19 83, Numerische ... think, squeezed 748 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5) Co...

Ngày tải lên: 24/12/2013, 12:16

... a 12 x 2 + a 13 x 3 + ···+a 1N x N =b 1 a 21 x 1 + a 22 x 2 + a 23 x 3 + ···+a 2N x N =b 2 a 31 x 1 + a 32 x 2 + a 33 x 3 + ···+a 3N x N =b 3 ··· ··· a M1 x 1 +a M2 x 2 +a M3 x 3 +···+a MN x N = ... columns of the matrix inverse of A (§2.1 and §2 .3) . • Calculation of the determinant of a square matrix A (§2 .3) . If M<N,orifM=Nbut the equations are degenerat...

Ngày tải lên: 15/12/2013, 04:15

... case of a single right-hand side vector):    a  11 a  12 a  13 a  14 0 a  22 a  23 a  24 00a  33 a  34 000a  44    ·    x 1 x 2 x 3 x 4    =    b  1 b  2 b  3 b  4    (2.2.1) Here ... identity matrix),Gaussianeliminationandbacksubstitutionatfirstglancerequire 1 3 N 3 (matrix reduction) + 1 2 N 3 (right-hand side manipulations) + 1 2 N 3 (N...

Ngày tải lên: 24/12/2013, 12:16