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.
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