An approach to integral equations by homotopy perturbation method

In this study, an application of the Homotopy Perturbation Method (HPM) is provided for Volterra and Fredholm integral equations and systems. The efficiency and practicality of HPM in solving the integral equations are examined through some examples. This thesis consists of four sections. In the first section, a literature review is given about the methods that will be used throughout the thesis. Secondly, an integral equation is introduced and a general classification is made. Third section reviews Adomian Decomposition Method (ADM), Successive Approximations Method (SAM), Direct Calculation Method (DCM), Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) as well as their applications to some integral equations. Finally, the efficiency and practicality of HPM is investigated with respect to the analytical and numerical results obtained from an example.