Asymptotical stability of numerical methods for semi-linear impulsive differential equations

Abstract

This paper is concerned with asymptotical stability of a class of semi-linear impulsive ordinary differential equations. First of all, sufficient conditions for asymptotical stability of the exact solutions of semi-linear impulsive differential equations are provided. Under the sufficient conditions, some explicit exponential Runge–Kutta methods can preserve asymptotically stability without additional restriction on stepsizes. Moreover, it is proved that some explicit Runge–Kutta methods can preserve asymptotical stability without additional restriction on stepsizes under stronger conditions.