A Quasilinearization Method For Integro-differential Equations And Rapid Convergence Of Solutions

In this paper, we mainly discussed initial value problem for integro-differential equations with impulse in Banach spaces and Volterra integro-differential equations, and also periodic boundary value problem for second order mixed differential equations by using the quasilin-earization method. There are four chapters in this paper.In Chapter 1 of this paper we introduce the background of the problem-researching and the recent development of the research in this field. The aim of Chapter 2 is to introduce the quasilinearization method for initial value problem of impulsive integro-differential equations and then establish rapid convergence of solutions.In Chapter 3 of this paper we introduce the quasilinearization method for initial value prob-lem of Volterra integro-differential equations and then establish rapid convergence of solutions.In Chapter 4 of this paper we introduce the quasilinearization method for the problem of first order integro-differential equations which is equivalent to that of second order mixed differential equations and rapid convergence of solutions is given.