Tài liệu Integration of Ordinary Differential Equations part 1 doc

... 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 ). ... http://www.nr.com or call 1- 800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). Chapter 16 . Integration of Ordinary Differential E...

Ngày tải lên: 15/12/2013, 04:15

... a i b ij c i c ∗ i 1 37 378 2825 27648 2 1 5 1 5 0 0 3 3 10 3 40 9 40 250 6 21 18575 48384 4 3 5 3 10 − 9 10 6 5 12 5 594 13 525 55296 5 1 − 11 54 5 2 − 70 27 35 27 0 277 14 336 6 7 8 16 31 55296 17 5 512 575 13 824 44275 11 0592 253 4096 512 17 71 1 4 j ... -0.9,b43 =1. 2, b 51 = -11 .0/54.0, b52=2.5,b53 = -70.0/27.0,b54=35.0/27.0, b 61= 16 31. 0/55296.0,b62 =1...

Ngày tải lên: 24/12/2013, 12:16

... 710 Chapter 16 . Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by ... Seinfeld, J. 19 71, Numerical Solution of Ordinary Differential Equations (New York: Academic Press). 16 .1 Runge-Kutta Method The formula for the Euler method is y n +1 =...

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 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge ... midpoint method is n +1. The formulas for the method are z 0 ≡ y(x) z 1 = z 0 + hf(x, z 0 ) z m +1 = z m 1 +2hf(x + mh, z m ) for m =1, 2, ,n 1 y(x+H)≈y n ≡ 1 2 [z n +z...

Ngày tải lên: 24/12/2013, 12:16

... nseq[IMAXX +1] ={0,2,4,6,8 ,10 ,12 ,14 ,16 ,18 }; int reduct,exitflag=0; d=matrix (1, nv ,1, KMAXX); err=vector (1, KMAXX); x=vector (1, KMAXX); yerr=vector (1, nv); ysav=vector (1, nv); yseq=vector (1, nv); if (eps ... tolerance. km=k -1; err[km]=pow(errmax/SAFE1 ,1. 0/(2*km +1) ); } if (k != 1 && (k >= kopt -1 || first)) { In order window. if (errmax < 1. 0) { Converged....

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 0-5 21- 4 310 8-5) Copyright (C) 19 88 -19 92 by Cambridge ... h[z 0 + 1 2 hf(x 0 ,y 0 )] y k +1 − 2y k + y k 1 = h 2 f (x 0 + kh, y k ),k =1, ,m 1 z m =(y m −y m 1 )/h + 1 2 hf(x 0 + H,y m ) (16 .5.2) 16 .5 Second-Order Conserv...

Ngày tải lên: 24/12/2013, 12:16

... -1. 0e29; eps1=SAFE1*eps; a [1] =nseq [1] +1; for (k =1; k<=KMAXX;k++) a[k +1] =a[k]+nseq[k +1] ; for (iq=2;iq<=KMAXX;iq++) { for (k =1; k<iq;k++) alf[k][iq]=pow(eps1,((a[k +1] -a[iq +1] )/ ((a[iq +1] -a [1] +1. 0)*(2*k +1) ))); } epsold=eps; nvold=nv; ... eigenvalue of C. On the other hand, implicit differencing gives y n +1 = y n + hy  n +1 (16 .6 .12 ) or y n +1 = (1+ Ch)...

Ngày tải lên: 24/12/2013, 12:16

... the differential equation y  n +1 = f(x n +1 ,y n +1 ) (16 .7 .10 ) be satisfied. The second of the equations in (16 .7.9) is hy  n +1 = hy  n +1 + αr 2 (16 .7 .11 ) and this will be consistent with (16 .7 .10 ) ... that  y n +1 = B · y n (16 .7.7) where the matrix B is B =    11 11 012 3 0 013 00 01    (16 .7.8) We now write the actual approximation to y n +1 th...

Ngày tải lên: 24/12/2013, 12:16

... Introduction A set of linear algebraic equations looks like this: a 11 x 1 + 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 ··· ... sides, the b’s, are changed (§2 .1 §2 .10 ). • Calculation of the matrix A 1 which is the matrix inverse of a square matrix A, i.e., A · A...

Ngày tải lên: 15/12/2013, 04:15

... above). For the case of a 4 × 4 matrix A, for example, equation (2.3 .1) would look like this:   α 11 000 α 21 α 22 00 α 31 α 32 α 33 0 α 41 α 42 α 43 α 44   ·   β 11 β 12 β 13 β 14 0 β 22 β 23 β 24 00β 33 β 34 000β 44   =   a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44   (2.3.2) We ... α ii (equation 2.3 .11 ) are...

Ngày tải lên: 24/12/2013, 12:16