Stability Of Numerical Methods For Nonlinear Impulsive Functional Differential Equations

Impulsive functional differential equations describe the system which occurs a sud-den change in some stages The sudden change process costs very little time,but has agreat influence on the operational stage of the entire system Impulsive functional dif-ferential equations are widely applied in high technology field There aJ'e hardly resultsofthe numerical methods for solving impulsive functional differential equations in litera-ture Therefore,it is of important theoretical and practical significance to investigate theproblemThis paper mainly considers the numerical stability ofimpulsive functional functionaldifferential equation as follows:whereτ>0 is a constant,B_k is a impulsive operator,0<τ₁<τ₂<…<τ_N-1<T areimpulsive points,△y|_t=τk=y(τ_k⁺)-y(τk),y(τ_k⁺)denotes the right limits ofy(t)atτ_k.In this paper,the 0-method for solving impulsive functional differential equation inBanach space is given The stability results ofθ-method axe obtained The stability ofRunge-Kutta methods for solving the impulsive functional differential equations in Hilbertspace is investigated The sufficient conditions of stability and asymptotical stability ofalgebraically stable RK-method are given The numerical results confirm our theoreticalanalysis...