Tài liệu Integration of Ordinary Differential Equations part 7 pptx
Tài liệu Integration of Ordinary Differential Equations part 7 pptx
... 6.02015 272 865#define C32 0.15 975 0684 673 #define C41 -1.856343618 677 #define C42 -8.50538085819#define C43 -2.084 075 13602#define B1 3.9 575 0 374 663#define B2 4.62489238836#define B3 0.6 174 772 63 873 #define B4 ... those of Shampinesimply by replacing the #define statements:#define GAM 0.231#define A21 2.0#define A31 4.52 470 82 073 6#define A32 4.16352 878 860#define C21 -5. 071 675 33 877 #define C31 6.02015 272 865#define ... E1 ( 17. 0/54.0)#define E2 (7. 0/36.0)#define E3 0.0#define E4 (125.0/108.0) 74 0Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...
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Tài liệu Integration of Ordinary Differential Equations part 2 pptx
... Springer-Verlag),Chapter 7. Lambert, J. 1 973 ,Computational Methods in Ordinary Differential Equations (New York: Wiley).Lapidus, L., and Seinfeld, J. 1 971 ,Numerical Solution of Ordinary Differential Equations (NewYork: ... 71 0Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... should recognize it as a statement about the 71 2Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright...
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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). ... 1-800- 872 -74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).Chapter 16. Integration of Ordinary Differential Equations 16.0 IntroductionProblems involving ordinary ... 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,...
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Tài liệu Integration of Ordinary Differential Equations part 3 doc
... 0331034094025062118 575 48384435310−9106512559413525552965 1 −115452− 70 27 35 27 0 277 143366 7 8163155296 175 512 575 1382444 275 1105922534096512 177 114j =12345Now ... -70 .0/ 27. 0,b54=35.0/ 27. 0,b61=1631.0/55296.0,b62= 175 .0/512.0,b63= 575 .0/13824.0,b64=44 275 .0/110592.0,b65=253.0/4096.0,c1= 37. 0/ 378 .0,c3=250.0/621.0,c4=125.0/594.0,c6=512.0/ 177 1.0,dc5 = - 277 .00/14336.0;float ... 71 4Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright...
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Tài liệu Integration of Ordinary Differential Equations part 4 ppt
... 72 2Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... pp. 201–222. [2]Shampine, L.F., and Watts, H.A. 1 977 , inMathematical Software III, J.R. Rice, ed. (New York:Academic Press), pp. 2 57 275 ; 1 979 ,Applied Mathematics and Computation,vol.5,pp. ... C.W. 1 971 ,Numerical Initial Value Problems in Ordinary Differential Equations (EnglewoodCliffs, NJ: Prentice-Hall). [1]Cash, J.R., and Karp, A.H. 1990,ACM Transactions on Mathematical Software,...
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Tài liệu Integration of Ordinary Differential Equations part 5 pdf
... 72 4Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... +H,whereHissupposed to be quite a large 72 6Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... (16.4.15)The α’s satisfy α(k, q +1) >α(k,q). 72 8Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright...
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Tài liệu Integration of Ordinary Differential Equations part 6 pdf
... 73 2Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... vol. 27, pp. 505–535. [3]16.5 Second-Order Conservative Equations Usually when you have a system of high-order differential equations to solve it is bestto reformulate 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 by differencing the equations...
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Tài liệu Integration of Ordinary Differential Equations part 8 pdf
... Predictor-corrector methods have been, we think, squeezed 74 8Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... steps, adjustingthe stepsize is difficult. 75 0Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright ... the differential equationyn+1= f(xn+1,yn+1)(16 .7. 10)be satisfied. The second of the equations in (16 .7. 9) ishyn+1= hyn+1+ αr2(16 .7. 11)and this will be consistent with (16 .7. 10)...
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Tài liệu Solution of Linear Algebraic Equations part 6 pptx
... x.2.5 Iterative Improvement of a Solution toLinear Equations Obviously it is not easy to obtain greater precision for the solution of a linearset than the precision of your computer’s floating-point ... Unfortunately, forlarge sets of linear equations, it is not always easy to obtain precision equal to, oreven comparable to, the computer’s limit. In direct methods of solution, roundofferrors accumulate, ... n] of the linear set of equations A · X = B.Thematrixa[1 n][1 n], and the vectorsb[1 n]andx[1 n]are input, as is the dimensionn.Also input isalud[1 n][1 n],theLU decomposition of aas...
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Tài liệu Solution of Linear Algebraic Equations part 7 docx
... also be aware of some of the special sparse forms that occur in thesolutionof partial differential equations in two or more dimensions. See Chapter 19.If your particular pattern of sparsity is ... makingthe same permutation of the columns of U,elementsofW,andcolumnsofV(orrows of VT), or (ii) forming linear combinations of any columns of U and V whosecorresponding elements of W happen to be ... combination of the set of equations thatwe are trying to solve. The resolution of the paradox is that we are throwing awayprecisely a combination of equations that is so corrupted by roundoff error...
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