An approach to nonlinear integral equations by homotopy perturbation method

In this thesis, we used theHomotopyPerturbation Method(HPM) to solve nonlinear Fredholm integral equations. We support the effectiveness of Homotop Perturbation Method(HPM) in solving integral equations by various examples.This thesis consist of four chapters. In the first chapter, we introduce the basic concepts and give a literatürereview.In the second chapter, we discuss the properties and give the classification of integral equations.In the third chapter, we review the properties of Homotopy Perturbation Method(HPM) and study their applications in integral equations.In addition to Homotopy Perturbation Method(HPM), we give the Direct Computation Method(DCM) , the Series Solution Method(SSM) andAdomian Decomposition Method(ADM) that are used to solve the nonlinear Fredholm integral equations. We then apply them to some integral equations. In the fourth chapter, we compare the analytical and numerical results in two different examples and we conclude that HomotopyPerturbation(HPM) is more effective and useful than the other methods.