Numerical oscillation and non-oscillation for differential equation with piecewise continuous arguments of mixed type

摘要

The paper deals with the oscillation and non-oscillation of the Runge–Kutta methods for a differential equation with piecewise continuous arguments of mixed type. The conditions of the oscillation and non-oscillation for the Runge–Kutta method are obtained. It is proved that oscillation of the analytic solution is not preserved by the Runge–Kutta method under any conditions. The conditions under which the non-oscillation of analytic solutions is preserved by the Runge–Kutta method are obtained. Some numerical experiments are given.