Tài liệu Integration of Ordinary Differential Equations part 2 pptx

... about the7 12 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 (C) 1988-19 92 by Cambridge ... 710Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)Copyright (C) 1988-19 92 by Cambridge ... the whole interval. Figure 16.1 .2 illustrates theidea. In equations, k1= hf(xn,yn)k 2 =hfxn+1 2 h, yn+1 2 k1yn+1= yn+ k 2 + O(h3)(16.1 .2) As indicated in the error term,...

Tài liệu Integration of Ordinary Differential Equations part 7 pptx

... (1.0 /2. 0)#define A21 2. 0#define A31 (48.0 /25 .0)#define A 32 (6.0 /25 .0)#define C21 -8.0#define C31 (3 72. 0 /25 .0)#define C 32 ( 12. 0/5.0)#define C41 (-1 12. 0/ 125 .0)#define C 42 (-54.0/ 125 .0)#define ... 4. 624 8 923 8836#define B3 0.61747 726 3873#define B4 1 .28 26 129 4 526 8#define E1 -2. 3 021 554 029 2#define E2 -3.07363448539#define E3 0.87 328 08018 02 #define E4 1 .28 26 129 4 526 8#define C1X GAM ... of Shampinesimply by replacing the #define statements:#define GAM 0 .23 1#define A21 2. 0#define A31 4. 524 70 820 736#define A 32 4.163 528 78860#define C21 -5.07167533877#define C31 6. 020 1 527 2865#define...

Tài liệu Integration of Ordinary Differential Equations part 1 doc

... odeintare 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). ... involving ordinary differential equations (ODEs) can always bereduced to the study of sets of ﬁrst-order differential equations. For example thesecond-order equationd 2 ydx 2 + q(x)dydx= ... variables.The generic problem in ordinary differential equations is thus reduced to thestudy of a set of N coupled ﬁrst-order differential equations for the functionsyi,i=1 ,2, ,N, having the general...

Tài liệu Integration of Ordinary Differential Equations part 3 doc

... 03310340940 25 0 621 1857548384435310−91065 125 59413 525 5 529 65 1 −11545 2 −70 27 35 27 0 27 71433667816315 529 61755 12 57513 824 4 427 51105 92 25340965 12 177114j = 123 45Now ... -0.9,b43=1 .2, b51 = -11.0/54.0, b 52= 2.5,b53 = -70.0 /27 .0,b54=35.0 /27 .0,b61=1631.0/5 529 6.0,b 62= 175.0/5 12. 0,b63=575.0/13 824 .0,b64=4 427 5.0/1105 92. 0,b65 =25 3.0/4096.0,c1=37.0/378.0,c3 =25 0.0/ 621 .0,c4= 125 .0/594.0,c6=5 12. 0/1771.0,dc5 ... -70.0 /27 .0,b54=35.0 /27 .0,b61=1631.0/5 529 6.0,b 62= 175.0/5 12. 0,b63=575.0/13 824 .0,b64=4 427 5.0/1105 92. 0,b65 =25 3.0/4096.0,c1=37.0/378.0,c3 =25 0.0/ 621 .0,c4= 125 .0/594.0,c6=5 12. 0/1771.0,dc5 = -27 7.00/14336.0;float dc1=c1 -28 25.0 /27 648.0,dc3=c3-18575.0/48384.0,dc4=c4-13 525 .0/5 529 6.0,dc6=c6-0 .25 ;float *ak2,*ak3,*ak4,*ak5,*ak6,*ytemp;ak2=vector(1,n);ak3=vector(1,n);ak4=vector(1,n);ak5=vector(1,n);ak6=vector(1,n);ytemp=vector(1,n);for...

Tài liệu Integration of Ordinary Differential Equations part 4 ppt

... 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 (C) 1988-19 92 by Cambridge ... Problems in Ordinary Differential Equations (EnglewoodCliffs, NJ: Prentice-Hall). [1]Cash, J.R., and Karp, A.H. 1990,ACM Transactions on Mathematical Software, vol. 16, pp. 20 1– 22 2. [2] Shampine, ... z0)zm+1= zm−1+2hf(x + mh, zm) for m =1 ,2, ,n−1y(x+H)≈yn≡1 2 [zn+zn−1+hf(x + H, zn)](16.3 .2) 16.3 Modiﬁed Midpoint Method 723 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

Tài liệu Integration of Ordinary Differential Equations part 5 pdf

... the sequencen =2, 4,6,8, 12, 16, 24 , 32, 48, 64, 96, ,[nj=2nj 2 ], (16.4.1)More recent work by Deuﬂhard [2, 3]suggests that the sequencen =2, 4,6,8,10, 12, 14, ,[nj=2j], (16.4 .2) is usually ... large 726 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 (C) 1988-19 92 by Cambridge ... 724 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 (C) 1988-19 92 by Cambridge...

Tài liệu Integration of Ordinary Differential Equations part 6 pdf

... 7 32 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 (C) 1988-19 92 by Cambridge ... 41, pp. 399– 422 . [2] Deuﬂhard, P. 1985,SIAM Review, vol. 27 , pp. 505–535. [3]16.5 Second-Order Conservative Equations Usually when you have a system of high-order differential equations to ... them as a system of ﬁrst-order equations, as discussed in §16.0. There isa particular class of equations that occurs quite frequently in practice where you can gainabout a factor of two in efﬁciency...

Tài liệu Integration of Ordinary Differential Equations part 8 pdf

... squeezed748Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)Copyright (C) 1988-19 92 by Cambridge ... difﬁcult.750Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)Copyright (C) 1988-19 92 by Cambridge ... RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)Copyright (C) 1988-19 92 by Cambridge University Press.Programs Copyright (C) 1988-19 92 by Numerical Recipes Software. Permission...

Tài liệu Solution of Linear Algebraic Equations part 2 ppt

... equationa11a 12 a13a14a 21 a 22 a 23 a 24 a31a 32 a33a34a41a 42 a43a44·x11x 21 x31x41x 12 x 22 x 32 x 42 x13x 23 x33x43y11y 12 y13y14y 21 y 22 y 23 y 24 y31y 32 y33y34y41y 42 y43y44=b11b 21 b31b41b 12 b 22 b 32 b 42 b13b 23 b33b431000010000100001 (2. 1.1)Here ... equationa11a 12 a13a14a 21 a 22 a 23 a 24 a31a 32 a33a34a41a 42 a43a44·x11x 21 x31x41x 12 x 22 x 32 x 42 x13x 23 x33x43y11y 12 y13y14y 21 y 22 y 23 y 24 y31y 32 y33y34y41y 42 y43y44=b11b 21 b31b41b 12 b 22 b 32 b 42 b13b 23 b33b431000010000100001 (2. 1.1)Here ... j and i  =2, 41 if i =2, j=41 if i =4,j =2 0 otherwise (2. 1.5)effects the interchange of rows 2 and 4. Gauss-Jordan elimination by row operations alone(including the possibility of partial pivoting)...

Tài liệu Solution of Linear Algebraic Equations part 6 pptx

... + δx)=b+δb (2. 5 .2) Subtracting (2. 5.1) from (2. 5 .2) givesA · δx = δb (2. 5.3)56Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 2. 5 Iterative Improvement of a Solution to Linear Equations 55Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)Copyright (C) 1988-19 92 by Cambridge ... reassuring. 2. 5 Iterative Improvement of a Solution to Linear Equations 57Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0- 521 -43108-5)Copyright (C) 1988-19 92 by Cambridge...

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