The Stability Of Nonlinear Stiff Delay Integro-differential Equations

This paper is devoted to studying the stability of nonlinear Stiff Delay Integro-differential Equations (DIDEs).For the system of delay with D (α,β,γ)-problem, we gained the conditions of stability and asymptotic stability. When the trapezoid formula was used to approach to Integration ,the stability of numerical methods such as one-leg methods, general linear method can be obtained. When the variable delay statisfies Lipschitz condition and the minimum Lipschitz contant L<1,we disscuss the stability of several numerical methods for variable delay Integro-differential Equations, and get the numerical results in this paper. Otherwise, the disspativity of DIDEs was studied by us.