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

Many practical problems can be modeled by impulsive functional diferential equationsystem, this system will occur a sudden change in some stage. Although the suddenchange process costs very little time, it has great influence on the entire system. Becauseof its applications are very broad, it is very important to investigate this problem.In this paper, we mainly considers the nonlinear impulsive functional diferentialequations in Banach space as followsk) denotes the left limits of y(t) at Ï„k. f:[0, T]×X×CX[Ï„, T]â†'X is a Lipschitzcontinuous function satisfingWe indicate this problem class as Dλ (α,β,γ,1,2), there are γ=(γ1,,γN). Particu-larly when λ=0, we call it as: D(α,β,γ,1,2).The main results obtained in this paper are as follows(1) We study the stability of the analytic solution of D(α,β,γ,1,2), and some stableresults are obtained.(2) We study the stability of Dλ (α,β,γ,1,2), some numerical stable results aregiven, and the numerical results confirm our theoretical analysis.