Linear multistep methods for impulsive differential equations

This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and two-step BDF method are of order p = 0 when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.