Stability Analysis Of Runge-Kutta Methods For A Class Of Nonlinear Impulsive Delay Differential Equations

Impulsive delay differential equations are widely used in many fields of science and engineering,such as automatic control,biology,medicine,chemistry,economics and so on.It is significant to study the numerical methods for impulsive delay differential equations.Due to the influence of impulse and time delay,the research of this kind of problem is very complicated and difficult.The related literature is not much,and mainly focus on linear problems and special nonlinear problems.In view of this,the present paper deals with the numerical stability of Runge-Kutta methods for a class of nonlinear impulsive delay differential equations.Firstly,the stability and asymptotic stability conditions for the theoretical solution of the problem are given.Secondly,the Runge-Kutta methods are applied to solve the problem.The results show that the algebraically stable Runge-Kutta methods can preserve the stability and asymptotic stability under certain conditions.Numerical experiments are give to confirm the theoretical results in the end.