Asymptotical stability of Runge–Kutta methods for advanced linear impulsive differential equations with piecewise constant arguments

This paper is concerned with a class of advanced linear impulsive differential equations with piecewise continuous argument. The sufficient and necessary condition for asymptotical stability of the exact solution is obtained. Under this condition, asymptotical stability of Runge–Kutta methods for this kind of equations is studied. Some numerical examples are given to confirm the theoretical results.