Approximate solutions of integral equations

It is well known that the theory and applications of the integral equations have an important role in applied mathematics. Many physical phenomenon can be modelled by various types of integral equations. This thesis is concerned with some numeric and semi-analytic methods for solving integral equations. In the present thesis the historical development of integral equations are given firstly. Then the method which was studied in a paper of KANWAL and K. C. LİU [1] and a paper of M. SEZER [2] , is applied to the linear Fredholm integral equation systems with variable coefficients.This thesis consists of sixth chapters. In the first chapter subject is introduced. In the second chapter the basic concepts are given which are necessary for the subject. In the third chapter, it is investigated a Taylor polynomial solutions of high order lineer Fredholm integral equations with variable coefficients which is given for integral equations. In the fourth chapter, some well known numeric and semi-analytic methods for Volterra integral equations have been given and the capacity of the methods have been investigated by the considered examples. The semianalytic methods (homotopy perturbation) have been applied to the several integral equations that solved by different methods and then exact solutions have been found. In the fifth chapter, some well known numeric and semi-analytic methods for Volterra integral equations have been given and the capacity of the methods have been investigated by the considered examples. The semianalytic methods (variational iteration) has been applied to the several integral equations that solved by different methods and then exact solutions have been obtained. In the final chapter, some of examples have been given in order to understand the homotopy perturbation and variational iteration methods.Key words: Fredholm integral equation systems, Integral equations, Taylor polynomials and series, Differential equations.