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

Impulsive differential equations(IDEs)can describe the practical problems with instantaneous mutation phenomenon.They are widely applied in the fields of science and technology,such as aerospace,control system,information science,life science,medicine,economics and so on.It is significant to research the theory and numerical methods for IDEs.Many results of the qualitative theory of IDEs has been found in literatures.However,there are a few results of the numerical methods for IDEs,and most of them are for linear problems or nonlinear problem in inner product space.In view of this,the present paper mainly studies the stability of numerical methods(Runge-Kutta methods)in more general Banach space.The main results are as follows:Firstly,the conditions of stability and asymptotic stability of a class of nonlinear impulsive differential equations in Banach space are derived.Secondly,the conditions for the stability and asymptotic stability of the explicit and diagonal implicit Runge-Kutta methods for nonlinear IDEs are ob-tained.The numerical experiments confirm the theoretical results.