Stability Of Runge-Kutta Methods For Multi-Delay Integro-Differential Equations

Delay Integro-Differential Equations (DIDEs)provide a powerful model of many phenomenain applied sciences, such as physics, engineering, biology, economics and so on. As we know,most of them cannot be solved analytically , so the numerical treatments of DIDEs becomes verynecessary. Furthermore, numerical stability is an important part in numerical analysis.The numerical solution of DIDEs has been the subject of intense research activity in the pastfew years,many numerical methods have been proposed for DIDEs,for example, Runge-Kuttamethods,θ-methods and so on. Also there has been some research in the fields of non-linearDIDEs. In this paper, we are concerned with Runge-Kutta methods for the multi-delay integro-differential equations.In Chapter 2, we discussed the necessary and sufficient conditions for the theoretical solu-tion's asymptotical stability for multi-delay integro-differential equations.Furthermore ,we get thesufficient conditions for the asymptotical stability for multi-delay integro-differential equations byRunge-Kutta methods .The major methods are as same as the methods for DDEs,and the estimateditems are applied when we treat the delay-items.In Chapter 3, we give some numerical examplesof DIDEs. These examples can confirm the theoretical results.