Tài liệu Integration of Ordinary Differential Equations part 4 ppt

... 722Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 ... important application as a part of the more powerful Bulirsch-Stoer technique, treated in §16 .4. You can thereforeconsider this section as a preamble to §16 .4. The number of right-hand side evaluations ... implement (16.3 .4) , since we will soon do even better.Now would be a good time to look back at the routine qsimp in 4. 2, andespecially to compare equation (4. 2 .4) with equation (16.3 .4) above. You...

Tài liệu Integration of Ordinary Differential Equations part 2 pptx

... 710Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 ... 1973,Computational Methods in Ordinary Differential Equations (New York: Wiley).Lapidus, L., and Seinfeld, J. 1971,Numerical Solution of Ordinary Differential Equations (NewYork: Academic ... statement about the712Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992...

Tài liệu Integration of Ordinary Differential Equations part 7 pptx

... 0.1597506 846 73#define C41 -1.856 343 618677#define C42 -8.50538085819#define C43 -2.0 840 7513602#define B1 3.957503 746 63#define B2 4. 6 248 9238836#define B3 0.61 747 7263873#define B4 1.282612 945 268#define ... a32g2)+(c31g1+ c32g2)/h(1/γh − f) · g 4 = f(y0+ a 41 g1+ a 42 g2+ a 43 g3)+(c 41 g1+ c 42 g2+ c 43 g3)/h(16.6. 24) In our implementation stiff of the Kaps-Rentrop algorithm, we have ... (25.0/108.0)#define B4 (125.0/108.0)#define E1 (17.0/ 54. 0)#define E2 (7.0/36.0)#define E3 0.0#define E4 (125.0/108.0) 740 Chapter 16. Integration of Ordinary Differential Equations Sample page...

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). ... auxiliary 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, ... conditions707708Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992...

Tài liệu Integration of Ordinary Differential Equations part 3 doc

... 033103 40 9 40 25062118575 48 3 84 435310−910651255 94 13525552965 1 −11 54 52−702735270277 143 36678163155296175512575138 24 442 75110592253 40 9651217711 4 j =12 345 Now ... -0.9,b43=1.2,b51 = -11.0/ 54. 0, b52=2.5,b53 = -70.0/27.0,b 54= 35.0/27.0,b61=1631.0/55296.0,b62=175.0/512.0,b63=575.0/138 24. 0,b 64= 442 75.0/110592.0,b65=253.0 /40 96.0,c1=37.0/378.0,c3=250.0/621.0,c4=125.0/5 94. 0,c6=512.0/1771.0,dc5 ... 7 14 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C)...

Tài liệu Integration of Ordinary Differential Equations part 5 pdf

... 7 24 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) ... 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 ... quite a large726Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992...

Tài liệu Integration of Ordinary Differential Equations part 6 pdf

... 732Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 ... 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 ... 41 , pp. 399 42 2. [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...

Tài liệu Integration of Ordinary Differential Equations part 8 pdf

... 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 -43 108-5)Copyright (C) ... is difﬁcult.750Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 108-5)Copyright (C) 1988-1992 ... withr1=0,r3=3 /4, andr 4 =1/6. The method is explicit because r1=0.TheAdams-Moultonmethod (16.7 .4) corresponds to the implicit four-value method withr1=5/12, r3=3 /4, andr 4 =1/6. Implicit...

Tài liệu Solution of Linear Algebraic Equations part 2 ppt

... equationa11a12a13a 14 a21a22a23a 24 a31a32a33a 34 a 41 a 42 a 43 a 44 ·x11x21x31x 41 x12x22x32x 42 x13x23x33x 43 y11y12y13y 14 y21y22y23y 24 y31y32y33y 34 y 41 y 42 y 43 y 44 =b11b21b31b 41 b12b22b32b 42 b13b23b33b 43 1000010000100001(2.1.1)Here ... equationa11a12a13a 14 a21a22a23a 24 a31a32a33a 34 a 41 a 42 a 43 a 44 ·x11x21x31x 41 x12x22x32x 42 x13x23x33x 43 y11y12y13y 14 y21y22y23y 24 y31y32y33y 34 y 41 y 42 y 43 y 44 =b11b21b31b 41 b12b22b32b 42 b13b23b33b 43 1000010000100001(2.1.1)Here ... and i =2 ,4 1 if i =2,j =4 1 if i =4, j=20 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 11 ppt

... many applications only the part (2.10 .4) of the algorithm is needed, so we separate it off into its own routine rsolv.100Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL ... describingthe ﬁt of data to a model; see, e.g., §15.6. In this, and many other applications,one often needsL−1. The lower triangle of this matrix can be efﬁciently found from the output of choldc:for ... typical systems of linear equations. However, we willmeet special cases where QR is the method of choice.2.10 QR Decomposition99Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

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