Numerical methods for impulsive differential equation

In this paper, the asymptotical stability of the numerical methods with the constant stepsize for impulsive differential equation ẋ(t)=αx,t≠k,t>0,△x=βx,t=k,x(0+0)=x0,x(0+0)=x0, where α≠0,β,x0∈R,1+β≠0α≠0,β,x0∈R,1+β≠0,k∈Nk∈N, are investigated. The asymptotical stability conditions of the analytic solution of this equation and the numerical solutions are obtained. Finally, some experiments are given.