discontinuous solutions of nonlinear differential equations

... Recently, there are a large number of papers dealing with the existence of solutions of nonlinear fractional differential equations by the use of techniques of nonlinear analysis (fixed point theore ... coupled system of nonlinear fractional differential equations. Appl Math Lett 2009, 22:64-69. 26. Gejji VD: Positive solutions of a system of nonlinear fractional differential equations. J Math ... uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations. Fixed Point Theory Appl 2010, 2010:1-17. 30. Babakhani A: Positive solutions for system of nonlinear...

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... made available soon. Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6 Oi ... ∈ (0, 1); 2. a sequence of complex numbers z n , |z n | < r; Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi Jianming 1,3 , ... order of entire solutions of some algebraic differential equations and improve the related results of Bergweiler, Barsegian, and others. We also estimate the growth order of entire solutions of a...

Ngày tải lên: 20/06/2014, 20:20

... class of second order differential equations, ” Journal of Differential Equations, vol. 82, no. 1, pp. 15–27, 1989. 9 W T. Li, “Oscillation of certain second-order nonlinear differential equations, ” ... u ∗ is a desired classical solution of 1.1. Since d>0, u ∗ is a nontrivial homoclinic solution. The proof is complete. Proof of Theorem 1.2. In the proof of Theorem 1.1, the condition that ... pages doi:10.1155/2010/470375 Research Article Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations Peng Chen and X. H. Tang School of Mathematical Sciences and Computing Technology,...

Ngày tải lên: 21/06/2014, 11:20

... made available soon. Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6 Oi ... solutions of some algebraic differential equations and improve the related results of Bergweiler, Barsegian, and others. We also estimate the growth order of entire solutions of a type system of a ... [w (m) (z)] r m , 17 [11] Gu, RM, Ding, JJ, Yuan, WJ: On the estimate of growth order of solutions of a class of systems of algebraic differential equations with higher orders. J. Zhanjiang Normal Univ. (in...

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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. ... 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, having ... 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 Press). 16.1...

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 Press). 16.1 ... 710 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... that derive from this basic 712 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

Ngày tải lên: 15/12/2013, 04:15

... generally useful stepper routine is this: One of the arguments of the routine will of course be the vector of dependent variables at the beginning of a proposed step. Call that y[1 n].Let us require ... ,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 0-521-43108-5) Copyright ... informationcan beobtained. Obviously, 720 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright...

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 0-521-43108-5) Copyright ... Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall). [1] Cash, J.R., and Karp, A.H. 1990, ACM Transactions on Mathematical Software , vol. 16, pp. 201– 222. ... modified midpoint method, which advances a vector of dependent variables y(x) from a point x to a point x + H by a sequence of n substeps each of size h, h = H/n (16.3.1) In principle, one could...

Ngày tải lên: 24/12/2013, 12:16

... extrapolate each component of a vector of quantities. 728 Chapter 16. Integration of Ordinary Differential Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... 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 differential equations. The ... method does an excellent job of feeling its way through rocky or discontinuous terrain. It is also an excellent choice for quick-and-dirty, low-accuracy solution of a set of equations. A second warning...

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