Stability Analysis Of Explicit And Diagonal Implicit Runge-Kutta Methods For Impulsive Delay Differential Equations In Banach Space

In many practical problems,the state of the system will instantaneously jump at certain points in time,called the pulse phenomenon.On the other hand,the current state of the system will be affected by the past state,known as the delay phenomenon.The system that co-exists between these two phenom-ena,the mathematical model is generally impulsive delay differential equations.Therefore,it is great significance to study the related theory of the impulsive delay differential equations.There have been many achievements in the study of the qualitative theory of impulsive delay differential equations,but the study of numerical methods has only just begun.The results are few and mainly aim at linear problems or nonlinear problems in Hilbert space.For this reason,this paper studies the numerical stability of the Runge-Kutta method in a more general Banach space and obtains the following main results.(1)The stability of the theoretical solution of a class of impulsive delay differential equations in Banach spaces is studied and the stability results are obtained.(2)The stability results of the explicit and diagonal implicit Runge-Kutta methods for solving the above problem class are obtained.Numerical experi-ments are given to confirm the theoretical results in the end.