Equivalent HPM with ADM and Convergence of the HPM to a Class of Nonlinear Integral Equations

Abstract

The purpose of this study is to implement homotopy perturbation

method, for solving nonlinear Volterra integral equations. In

this work, a reliable approach for convergence of the HPM when applied

to a class of nonlinear Volterra integral equations is discussed.

Convergence analysis is reliable enough to estimate the maximum absolute

truncated error of the series solution. The results obtained by

using HPM, are compared to those obtained by using Adomian decomposition

method alone. The numerical results, demonstrate that HPM

technique, gives the approximate solution with faster convergence rate

and higher accuracy than using the standard ADM.