Application Of B-theory Of Numerical Methods For Functional Differential Equations To Stiff Integro-differential Equations

Stability of theoretical and numerical solution to stiff integro-differential equa-tions(IDEs)and to stiff integro-differential equations(SIDEs) of integral limit which depends on state function y(t)are discussed in this paper. Because the research of IDEs is difficult,so far only various special cases of problem(l), such as linear IDEs and nonlinear IDEs with special form have been research in literatures at home and abroad. In this paper we apply B- theory of numerical methods for stiff Volterra functional differential equations(VFDEs) to nonlinear stiff IDEs of the form (1) and (2), and the main results obtained are as follows:(1) We obtain the stability,the generalized strict contractivity and asymptotic stability properties of the problem(1)and also get the stability property of the problem(2).(2) We get a series of new mumerical stability and convergence results of Runge-kutta methods and General linear methods for IDEs of the form (1) and (2).Most of theories results above have still not been research in literatures at home and abroad so far. Therefore, there are innovative property and important theory and practical value .(3) Finally ,we carry on the mumerical test by using several kinds of mumerical methods for IDEs and SIDEs , and the mumerical results have supported the theories results obtained in this paper.