nonlinear ordinary differential equations jordan smith solutions

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Ngày tải lên: 19/03/2015, 08:49

... 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...

Ngày tải lên: 15/12/2013, 04:15

... 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...

Ngày tải lên: 24/12/2013, 12:16

... 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

... method, discussed in this section, is the best known way to obtain high-accuracy solutions to ordinary differential equations with minimal computational effort. (A possible exception, infrequently ... 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...

Ngày tải lên: 24/12/2013, 12:16

... general case implicit methods give better stability. 742 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... rule: y n+1 − y n−1 =2hf  y n+1 + y n−1 2  (16.6.29) 738 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] Kaps, P., and Rentrop, P. 1979, Numerische...

Ngày tải lên: 24/12/2013, 12:16

... 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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Ngày tải lên: 31/03/2014, 15:56

... system. Moreover, if I = R, solutions exist for all t ∈ R by Theorem 2.12. Now observe that linear combinations of solutions are again solutions. Hence the set of all solutions forms a vector space. ... 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: ... manuscript provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental...

Ngày tải lên: 31/03/2014, 15:56

... 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 on ... 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 ... derivatives). AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS This refreshing, introductory textbook covers standard techniques for solving ordi- nary differential equations, as well as introducing...

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Ngày tải lên: 12/06/2014, 16:08

... the existence of solutions for first-order nonlinear integro -differential equations with boundary value conditions. Our methods to prove the existence of solutions involve new differential inequalities and ... order ordinary differential equations. Math Inequal Appl. 6, 477–485 (2003) 23. Luo, ZG, Shen, JH, Nieto, JJ: Antiperiodic boundary value problem for first -order impulsive ordinary differential equations. ... type on time scales. Nonlinear Anal. 68, 127–138 (2008). doi:10.1016/j.na.2006.10.036 16. Xu, H, Nieto, JJ: Extremal solutions of a class of nonlinear integro -differential equations in Banach...

Ngày tải lên: 21/06/2014, 02:20

... pages doi:10.1155/2011/684542 Research Article Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval Xuemei Zhang, 1 Xiaozhong Yang, 1 and Meiqiang Feng 2 1 Department ... second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times. Consider the following boundary value problem for second-order nonlinear ... impulsive di fferential equations, ” Applied Mathematics and Computation, vol. 202, no. 2, pp. 550–561, 2008. 19 T. Jankowski, “Existence of solutions for second order impulsive differential equations with...

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