High order Runge-Kutta methods for impulsive delay differential equations

The purpose of this paper is to obtain high order Runge-Kutta methods for nonlinear impulsive delay differential equations (IDDEs). In order to achieve the purpose, continuity and smoothness of the exact solutions of IDDEs are analyzed. And then the discontinuous points and non-smooth points are chosen as a part of the nodes of the Runge-Kutta methods. Furthermore, it is proved that the pth order Runge-Kutta method for IDDEs is also convergent of order p. And some simple numerical examples are given to demonstrate the theoretical results.