Preservation of Oscillations in the Runge-Kutta Method for a Type of Advanced Differential Equation

Abstract

This article is concerned with the preservation of oscillations for differential equations with piecewise constant arguments of advanced type. By using the Runge-Kutta method, new oscillation conditions for numerical solution are established. We prove that oscillations of the analytic solution are preserved by the numerical solution in the Runge-Kutta method under some conditions. Some experiments are given.

Keywords:

• Delay differential equation
• Numerical solution
• Oscillation
• Runge-Kutta methods

Mathematics Subject Classification:

• 34C10
• 39B72