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International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.3, No.4, Jun. 2011

Numerical Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Alternately Advanced and Retarded Type

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Author(s)

Qi Wang, FengLian Fu

Index Terms

Runge-Kutta methods;numerical solution;piecewise constant arguments;oscillation

Abstract

The purpose of this paper is to study the numerical oscillations of Runge-Kutta methods for the solution of alternately advanced and retarded differential equations with piecewise constant arguments. The conditions of oscillations for the Runge-Kutta methods are obtained. It is proven that the Runge-Kutta methods preserve the oscillations of the analytic solution. In addition, the relationship between stability and oscillations are shown. Some numerical examples are given to confirm the theoretical results.

Cite This Paper

Qi Wang, FengLian Fu,"Numerical Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Alternately Advanced and Retarded Type", International Journal of Intelligent Systems and Applications(IJISA), vol.3, no.4, pp.49-55, 2011. DOI: 10.5815/ijisa.2011.04.07

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