Convergence Analysis Of Runge-Kutta Methods For Impulsive Differential Equations

Impulsive differential equations(IDEs)are widely used in aerospace?control systems?biology?medicine?economics and so on.Since their analytical solutions are generally difficult to obtain,it is significant to study the numerical methods for IDEs.At present,there are many results in the study of the stability of numerical methods for IDEs,however,the study of convergence is relatively fewer.In view of this,the paper focuses on the convergence of numerical methods for IDEs.The classical convergence results(for non-stiff problems)and B-convergence results(for stiff problems)of Runge-Kutta methods for nonlinear IDEs and a class of nonlinear impulsive pantograph differential equations have been obtained.Numerical experiments confirm the theoretical results.