Stability of Runge–Kutta methods for linear impulsive delay differential equations with piecewise constant arguments

This paper is concerned with a class of linear impulsive delay differential equations with piecewise continuous argument. The conditions for stability of the exact solution are obtained. Under these conditions, it is proven that the θθ-method preserves stability of the equations. Furthermore, stability of Runge–Kutta methods for this kind of equations is studied. Some numerical examples are given to confirm the theoretical results.