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

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.