The analytic and numerical stability of stiff impulsive differential equations in Banach space

In this paper, we first introduce the test problem classes with respect to the initial value problems of nonlinear stiff impulsive differential equations in Banach spaces. The stability and asymptotic stability results of the analytic solution of the above-mentioned problems are obtained. As an example of discretization methods, the numerical stability and asymptotic stability results of the implicit Euler method are also given.