linear ordinary differential equations pdf

... solutions to ordinary differential equations with minimal computational effort. (A possible exception, infrequently encountered in practice, is discussed in Đ16.7.) 726 Chapter 16. Integration of Ordinary ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Đ 6.1.4. Stoer, J., and Bulirsch, R. ... Method The techniques described in this section are not for differential equations containing nonsmooth functions. For example, you might have a differential equation whose right-handside involves a...

Ngày tải lên: 24/12/2013, 12:16

... Second-Order Conservative Equations Usually when you have a system of high-order differential equations to solve it is best to reformulate them as a system of rst-order equations, as discussed ... 27, pp. 505–535. 16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential equation, the possibility of a stiff set of equations arises. Stiffness occurs in ... reason for this is explained below). This is so even 732 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

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... Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall), Chapter 9. [1] Shampine, L.F., and Gordon, M.K. 1975, Computer Solution of Ordinary Differential Equations. The ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Kaps, P., and Rentrop, P. 1979, Numerische ... Predictor-corrector methods have been, we think, squeezed 752 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

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... Integration of Ordinary Differential Equations 16.0 Introduction Problems involving ordinary differential equations (ODEs) can always be reduced to the study of sets of first-order differential equations. ... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic ... 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 the functions y i ,i=1,2, ,N,...

Ngày tải lên: 15/12/2013, 04:15

... 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley). Lapidus, L., and Seinfeld, J. 1971, Numerical Solution of Ordinary Differential Equations (New York: Academic ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). Acton, F.S. 1970, Numerical Methods ... 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

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... 722 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Cash, J.R., and Karp, A.H. 1990, ACM ... ,n−1 y(x+H)≈y n ≡ 1 2 [z n +z n−1 +hf(x + H, z n )] (16.3.2) 714 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...

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... 722 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Cash, J.R., and Karp, A.H. 1990, ACM ... ofthe modied midpointmethod tothe Bulirsch-Stoertechnique (Đ16.4) derives from a deep result about equations (16.3.2), due to Gragg. It turns out that the error of (16.3.2), expressed as a power...

Ngày tải lên: 24/12/2013, 12:16

... implicit methods holds only for linear systems, but even in the general case implicit methods give better stability. 742 Chapter 16. Integration of Ordinary Differential Equations Sample page from ... hf(y n+1 )(16.6.15) In general thisissome nasty set of nonlinear equationsthathasto be solvediteratively at each step. Suppose we try linearizing the equations, as in Newton’s method: y n+1 = y n + h  f(y n )+ ∂f ∂y     y n ·(y n+1 − ... REFERENCES AND FURTHER READING: Gear, C.W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Kaps, P., and Rentrop, P. 1979, Numerische...

Ngày tải lên: 24/12/2013, 12:16

... conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous linear flow. Then we establish the Frobenius method for linear equations in the com- plex domain and ... = x 0 is transformed into a linear system of equations by the Laplace transform. 3.3. General linear first order systems We begin with the study of the homogeneous linear first order system ˙x(t) ... the Melnikov method for homoclinic orbits. Keywords and phrases. Ordinary differential equations, dynamical systems, Sturm-Liouville equations. Typeset by A M S-L A T E X and Makeindex. Version:...

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... Summary of phase portraits for linear equations 301 31.1 *Jordan canonical form 301 Exercises 305 Part VI Coupled nonlinear equations 307 32 Coupled nonlinear equations 309 32.1 Some comments ... a systematic way. 3.1 Ordinary and partial differential equations The most significant distinction is between ordinary and partial differential equa- tions, and this depends on whether ordinary or partial ... for nonlinear equations 89 10.1 Exact equations 89 10.2 Substitution methods 94 Exercises 97 Part II Second order linear equations with constant coefficients 99 11 Second order linear equations: ...

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... second-order superlinear neutral differential equations. Math Slovaca. (to appear) 12. Li, T, Han, Z, Zhang, C, Li, H: Oscillation criteria for second-order superlinear neutral differential equations. ... neutral delay differential equations. Adv Differ Equ. 2010,1–9 (2010) 14. Li, T, Thandapani, E: Oscillation of solutions to odd-order nonlinear neutral functional differential equations. Electron ... non -linear neutral delay differential equations of higher order for p(t) = ± 1. Arch Math. 40, 359–366 (2004) 16. Tang, S, Li, T, Thandapani, E: Oscillation of higher-order half -linear neutral differential...

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... differential equations, ” Journal of Differential Equations, vol. 189, no. 2, pp. 396–411, 2003. 2 R. D. Nussbaum, “A Hopf global bifurcation theorem for retarded functional differential equations, ” Transactions ... pp. 139–164, 1978. 3 J. L. Kaplan and J. A. Yorke, Ordinary differential equations which yield periodic solutions of differential delay equations, ” Journal of Mathematical Analysis and Applications, ... of differential delay equations, ” Nonlinear Analysis: Theory, Methods & Applications, vol. 35, no. 4, pp. 457–474, 1999. 9 J. Li and X Z. He, “Multiple periodic solutions of differential delay equations...

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