### 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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#### 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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