Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments

Authors:
Z. W. Yang;M. Z. Liu;Juan J. Nieto
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China and Science Research Center, The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technolog ...;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China and Science Research Center, The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technolog ...;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China and Science Research Center, The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technolog ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 7
Cited 1

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Abstract

In this paper we deal with the numerical solutions of Runge-Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green's function. It is shown that Runge-Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.