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 -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 therefore consider this section as a preamble to §16 .4. The number of right-hand s...

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... 710 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) 1988-1992 ... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York:...

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... 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 ... a 32 g 2 )+(c 31 g 1 + c 32 g 2 )/h (1/γh − f  ) · g 4 = f(y 0 + a 41 g 1 + a 42 g 2 + a 43 g 3 )+(c 41 g 1 + c 42 g 2 + c 43 g 3 )/h (16.6. 24) In our...

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... 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...

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... 0 3 3 10 3 40 9 40 250 621 18575 48 3 84 4 3 5 3 10 − 9 10 6 5 125 5 94 13525 55296 5 1 − 11 54 5 2 − 70 27 35 27 0 277 143 36 6 7 8 1631 55296 175 512 575 138 24 442 75 110592 253 40 96 512 1771 1 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=25...

Ngày tải lên: 24/12/2013, 12:16

... 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 sequence n =2 ,4, 6,8,12, 16, 24, 32, 48 , 64, 96, ,[n j =2n j−2 ], (16 .4. 1) More recent work by Deuflhard [2,3] suggests that the sequence n =2 ,4, 6,8,10, 12, 14, ,[n j =2j], (16 .4. 2) is usually...

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... 732 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) 1988-1992 ... them as a system of first-order equations, as discussed in §16.0. There is a particular class of equations that occurs quite frequently in practice where you can gain about a factor of two...

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... 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. 750 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521 -43 10...

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... equation   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   ·     x 11 x 21 x 31 x 41      x 12 x 22 x 32 x 42      x 13 x 23 x 33 x 43      y 11 y 12 y 13 y 14 y 21 y 22 y 23 y 24 y 31 y 32 y 33 y 34 y 41 y 42 y 43 y 44     =     b 11 b 21 b 31 b 41      b 12 b 22 b 32 b 42      b...

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... many applications only the part (2.10 .4) of the algorithm is needed, so we separate it off into its own routine rsolv. 100 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL ... describing the fit of data to a model; see, e.g., §15.6. In this, and many other applications,one often needs L −1 . The lower triangle of this matrix can be efficiently found from...

Ngày tải lên: 15/12/2013, 04:15