Numerical oscillation and non-oscillation analysis of the mixed type impulsive differential equation with piecewise constant arguments

The purpose of this paper is to study oscillation and non-oscillation of Runge-Kutta methods for linear mixed type impulsive differential equations with piecewise constant arguments. The conditions for oscillation and non-oscillation of numerical solutions are obtained. Also conditions under which Runge-Kutta methods can preserve the oscillation and non-oscillation of linear mixed type impulsive differential equations with piecewise constant arguments are obtained. Moreover, the interpolation function of numerical solutions is introduced and the properties of the interpolation function are discussed. It turns out that the zeros of the interpolation function converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge-Kutta method. To confirm the theoretical results, the numerical examples are given.