ORDINARY DIFFERENTIAL EQUATIONS

... 708 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 ... drivers Section 16 .6 of this chapter treats the subject of stiff equations, relevant both to ordinary differential equations and also to partial differential equ...

Ngày tải lên: 15/12/2013, 04:15

... http://www.nr.com or call 1-800-8 72- 7 423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America) x2 x1 7 12 Chapter 16 Integration of Ordinary Differential Equations yn yn + Figure ... yout[i]=y[i]+h6*(dydx[i]+dyt[i] +2. 0*dym[i]); weights free_vector(yt,1,n); free_vector(dyt,1,n); free_vector(dym,1,n); 714 Chapter 16 Integration of Ordinary Diff...

Ngày tải lên: 15/12/2013, 04:15

... Method i ci bij 1 5 3 10 40 40 10 − 10 5 − 11 54 − 70 27 35 27 1 631 55296 175 512 575 138 24 44275 110592 2 53 4096 2825 27648 j= 0 250 621 18575 4 838 4 125 594 135 25 55296 277 1 433 6 512 1771 Now that ... b51 = -11.0/54.0, b52=2.5,b 53 = -70.0/27.0,b54 =35 .0/27.0, b61=1 631 .0/55296.0,b62=175.0/512.0,b 63= 575.0/ 138 24.0, b64=44275.0/110592.0,b65=2 53. 0/4096.0,c1 =37 .0 /37 8.0,...

Ngày tải lên: 24/12/2013, 12:16

... powers of h, 7 24 Chapter 16 Integration of Ordinary Differential Equations } CITED REFERENCES AND FURTHER READING: Gear, C.W 1971, Numerical Initial Value Problems in Ordinary Differential Equations ... compare equation (4. 2 .4) with equation (16.3 .4) above You will see that the transition in Chapter to the idea of Richardson extrapolation, as embodied in Romberg inte...

Ngày tải lên: 24/12/2013, 12:16

... in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), §6.2 Deuflhard, P 1983, Numerische Mathematik, vol 41, pp 399–422 [2] Deuflhard, P 19 85, SIAM Review, vol 27, pp 50 5 53 5 ... method a degree of robustness for problems with discontinuities Let us remind you once again that scaling of the variables is often crucial for successful integration of different...

Ngày tải lên: 24/12/2013, 12:16

... Chapter 16 Integration of Ordinary Differential Equations Note that for compatibility with bsstep the arrays y and d2y are of length 2n for a system of n second-order equations The values of y are ... = ( 16. 6.2) v = −y + z ( 16. 6.3) By means of the transformation u = 2y − z we find the solution u = 2e−x − e−1000x v = −e−x + e−1000x ( 16. 6.4) If we integrated the system...

Ngày tải lên: 24/12/2013, 12:16

... 4.52 470 82 073 6 A32 4.16352 878 860 C21 -5. 071 675 33 877 C31 6.02015 272 865 C32 0.15 975 0684 673 C41 -1.856343618 677 C42 -8.50538085819 C43 -2.084 075 13602 B1 3.9 575 0 374 663 B2 4.62489238836 B3 0.6 174 772 63 873 ... in stiff"); 74 2 Chapter 16 #define #define #define #define #define C2X C3X C4X A2X A3X Integration of Ordinary Differential Equations -0.396296 677 520e-01...

Ngày tải lên: 24/12/2013, 12:16

... RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-431 08- 5) Copyright (C) 1 988 -1992 by Cambridge University Press.Programs Copyright (C) 1 988 -1992 by Numerical Recipes Software Permission ... RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-431 08- 5) Copyright (C) 1 988 -1992 by Cambridge University Press.Programs Copyright (C) 1 988 -1992 by Numerical Recipes Softw...

Ngày tải lên: 24/12/2013, 12:16

... interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits Keywords and phrases Ordinary differential equations, dynamical systems, Sturm-Liouville equations ... classification 3 4-0 1 Abstract This manuscript provides an introduction to ordinary differential equations and dynamical systems We start with some simple examples of...

Ngày tải lên: 31/03/2014, 15:56

Ngày tải lên: 12/06/2014, 16:08

... 139–164, 1978 J L Kaplan and J A Yorke, Ordinary differential equations which yield periodic solutions of differential delay equations,” Journal of Mathematical Analysis and Applications, vol 48, ... is a periodic solution of 1.2 with period T 2.20 2π Journal of Inequalities and Applications Acknowledgments The authors would like to thank the referee for careful reading of...

Ngày tải lên: 22/06/2014, 02:20

... Proof By the continuation of solutions and the singularity of ᏷ at the point P0 , the set ᏷(P0 ) = ∅ Taking into account the nature of the vector field and the definition of the singularity of ... ,ρ0 ) ∈ E ⊆ ∂ω and the family ᐄ(P0 ) of all noncontinuable solutions of the initial value problem (2.6) By the continuity of the nonlinearity and the nature of the vector...

Ngày tải lên: 22/06/2014, 22:20

... more accurate solutions The size of the integration interval also influences the accuracy of the solutions (should be less than 10% of the time constant) • • st Solutions of sets of order ODEs ... interval × function of gradient • This is the basis for a family of algorithms used to provide numerical solutions of ODEs • A particular class is the Runge-Kutta algorithm...

Ngày tải lên: 19/03/2015, 08:49