He’s homotopy perturbation method: An effective tool for solving a nonlinear system of two-dimensional Volterra–Fredholm integral equations

Abstract

In this paper, we conducted a comparative study between He’s homotopy perturbation method (HPM) and the Adomian decomposition method (ADM) for solving a nonlinear system of two-dimensional Volterra–Fredholm integral equations. He’s homotopy perturbation method is implemented in a straightforward manner. The proper implementation of He’s homotopy perturbation method can extremely minimize the size of computational work compared with the existing traditional techniques. The analysis is accompanied by examples that demonstrate the comparison, and shows the pertinent features of the homotopy perturbation technique.