Stability Analysis of Multistage One-Step Multiderivative Methods for Nonlinear Impulsive Differential Equations in Banach Spaces

Abstract

In this paper, we first introduce the problem class $K^{\left(p\right)}\left(\mu ,\lambda ,\zeta \right)$ with respect to the initial value problems of nonlinear impulsive differential equations in Banach spaces. The stability and asymptotic stability results of the analytic solution of the problem class $K^{\left(p\right)}\left(\mu ,\lambda ,\zeta \right)$ are obtained. Then, the numerical stability and asymptotic stability conditions of multistage one-step multiderivative methods are also given. Two numerical experiments are given to confirm the theoretical results in the end.