Convergence Analysis Of Multistep Methods For Impulsive Differential Equations

Impulsive differential equations(IDEs)are widely used in fields of ecological dynamics,medicine,economics,automatic control,etc.Generally,due to difficulty in obtaining the analytical solutions of IDEs,it is necessary to study numerical methods for IDEs.In order to solve IDEs,numerous achievements are concerned with one-step methods,but few of them are involved in multistep methods.In view of this,the present paper mainly deals with the convergence of multistep methods for IDEs.The major results are as follows:(1)If multistep methods for solving ordinary differential equations(ODEs),including linear multistep methods,one-leg methods,multistep Runge-Kutta methods,are classical convergent of order r,then the methods for solving IDEs are also classical convergent of order r.If multistep methods for solving ODEs are -convergent of order r,then the methods for solving stiff IDEs are also -convergent of order r.(2)The convergence of multistep methods for a class of nonlinear impulsive delay differential equations is similar to the previous one.Meanwhile,numerical examples also confirm the theoretical results.