Tài liệu Integration of Ordinary Differential Equations part 6 pdf

... 732 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... 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 equations,...

Ngày tải lên: 24/12/2013, 12:16

... +H,whereHissupposed to be quite a large 7 26 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... using ¯ H k . The criterion of being “too small” is taken to be H k α(k, q +1)<H ( 16. 4.15) The α’s satisfy α(k, q +1) >α(k,q). 728 Chapter 16. Integration of...

Ngày tải lên: 24/12/2013, 12:16

... methods have been, we think, squeezed 748 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... adjusting the stepsize is difficult. 750 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

Ngày tải lên: 24/12/2013, 12:16

... America). Chapter 16. Integration of Ordinary Differential Equations 16. 0 Introduction Problems involving ordinary differential equations (ODEs) can always be reduced to the study of sets of first-order differential ... odeint are drivers. Section 16. 6 of this chapter treats the subject of stiff equations, relevant both to ordinary differential equations and...

Ngày tải lên: 15/12/2013, 04:15

... Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic Press). 16. 1 Runge-Kutta ... 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

Ngày tải lên: 15/12/2013, 04:15

... +2) are required. This accounts for the 7 16 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... a 2 h, y n + b 21 k 1 ) ··· k 6 =hf(x n + a 6 h, y n + b 61 k 1 + ···+b 65 k 5 ) y n+1 = y n + c 1 k 1 + c 2 k 2 + c 3 k 3 + c 4 k 4 + c 5 k 5 + c 6 k 6 + O(h...

Ngày tải lên: 24/12/2013, 12:16

... 722 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... usefulness ofthe modified midpointmethod tothe Bulirsch-Stoertechnique (§ 16. 4) derives from a “deep” result about equations ( 16. 3.2), due to Gragg. It turns out that the error of ( 16. 3.2), expressed ......

Ngày tải lên: 24/12/2013, 12:16

... 6. 02015272 865 #define C32 0.15975 068 467 3 #define C41 -1.8 563 4 361 867 7 #define C42 -8.50538085819 #define C43 -2.0840751 360 2 #define B1 3.9575037 466 3 #define B2 4 .62 4892388 36 #define B3 0 .61 7477 263 873 #define ... v(0) = 0 ( 16. 6.2) By means of the transformation u =2y−zv=−y+z ( 16. 6.3) we find the solution u =2e −x −e −1000x v = −e −x + e −1000x ( 16. 6.4) If we integ...

Ngày tải lên: 24/12/2013, 12:16

... Sciences (New York: McGraw-Hill), Program B-2, p. 298. Westlake, J.R. 1 968 , A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). Ralston, A., and Rabinowitz, P. 1978, A ... is called backsubstitution.Thecom- bination of Gaussian elimination and backsubstitution yields a solution to the set of equations. The advantage of Gaussian eliminat...

Ngày tải lên: 24/12/2013, 12:16

... R 1 × a 12 R 4 = a 21 × R 3 R 5 = R 4 − a 22 R 6 = Inverse(R 5 ) c 12 = R 3 × R 6 c 21 = R 6 × R 2 R 7 = R 3 × c 21 c 11 = R 1 − R 7 c 22 = −R 6 (2.11 .6) ... 5.3, 12 .6. [2] 2.11 Is Matrix Inversion an N 3 Process? We close this chapter with a little entertainment, a bit of algorithmic prestidig- itation which probes more deeply into the subject of matrix ... (outside North Ame...

Ngày tải lên: 24/12/2013, 12:16