Convergence, consistency and zero stability of impulsive one-step numerical methods

Abstract

Impulsive one-step numerical methods are defined in the present paper, especially, a common and widely used numerical form generalised from Runge-Kutta methods defined as impulsive Runge-Kutta methods. And it is proved that a consistent and zero-stable method thus convergent. Moreover, it is also proved that an impulsive one-step numerical method is convergent of order p if the corresponding method is pth order. Another equivalent form of impulsive one-step numerical methods are also introduced. In addition, numerical experiments are provided to illustrate the advantage of impulsive Runge-Kutta methods.