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

Impulsive differential equations (IDEs) can describe the phenomena of the real world with instantaneous mutation. They are widely used in the fields of science and technology, such as aerospace, information science, control systems, life science, medicine and so on. It is significant to research the theory and numerical methods for IDEs. There have been many results on the qualitative theory of IDEs. However, there are a few results of the numerical methods for IDEs, and most of them are for linear problems. In view of this, the present paper mainly studies the stability of numerical methods (Runge-Kutta methods) for nonlinear impulsive differential equations. The main results are as follows:Firstly, the conditions of stability and asymptotic stability of nonlinear impulsive differential equations in Banach space are derived, and the relevant results of the existing literature are improved. The stability of the implicit Euler method are obtained.Secondly, the conditions for the stability and asymptotic stability of the Runge-Kutta methods for nonlinear IDEs are obtained. The numerical experi-ments confirm the theoretical results.