An Approximate Method For Solving Integral Equations And Integro-differential Equations

In this study, we mainly discussed several kinds of integral equations and integro-differential equations. This paper proposes a simple and effective approximation method for those equations, moreover, an integro-differential equation can be converted approximately to a system of linear equations for the unknown function, so it can be obtained abundance of numerical results by using common computer,and we have given the error analysis of the approximation of one kind of equations. Some examples are given to illustrate the accuracy of this method. There are five 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 an approximate solution of a class of twodimensional Fredholm integral equations, and an error analysis of the approximation of equation is given.In Chapter 3 of this paper we introduce an approximate solution of a class of Fredholm integro-differential equations and Volterra integro-differential equations separately, several examples are given to test the accuracy of this method.In Chapter 4 of this paper we introduce an approximate solution of a class of nonlinear integral equations.In the fifth chapter, the above studied problems are concluded. Illustrative examples demonstrate that the present method is simple, high accuracy and efficent. Along this idea of thought, more problem of approximate solution and the theory of the method can be perfect.