Numerical solutions of the integral equations: Homotopy perturbation method and Adomian’s decomposition method

Abstract

In this paper, a homotopy perturbation method is proposed to solve non-singular integral equations. Comparisons are made between Adomian's decomposition method and the proposed method. It is shown, Adomian's decomposition method is a homotopy, only. Finally, by using homotopy perturbation method, a new iterative scheme, like Adomian's decomposition method, is proposed for solving the non-singular integral equations of the first kind. The results reveal that the proposed method is very effective and simple.