Solution of integral equations through Homotopy Perturbation Method

In this study Homotopy Perturbation Method (HPM)is investigated which is one of the recently developed methods for solving integral equations numerically and analytically. Its effectiveness and practicality in solving integral equations is shown with some specific examples.This text consists of four sections where the first section includes some introductory explanations about HPM as well as the aim and outcomes of this study. In the second section a classification of integral equations is given and their properties are explained, while in the subsequent section characteristics of HPM and its use in solving integral equations are handled. Also; some other numerical methods such as Direct Method, Series Solution Method, Adomian Decomposition Method, Variational Iteration Method and Differential Transform Method are presented, which are also used to obtain numerical solutions to integral equations. HPM and other methods counted above are employed in solving some integral equations numerically and results obtained through their application are compared with each other. In fourth and last section some judgments are made with regard to effectiveness and practicality of HPM in the light of the applications and their results given in the preceding section.Keywords:Integral equations, Homotopy perturbation method