Is homotopy perturbation method the traditional Taylor series expansion

Abstract

The search for a better and easy to use tool for the solution of nonlinear equations illuminating the nonlinear phenomena of our life is continuing. Various methods therefore were proposed to find approximate solutions. One of the most recent popular technique is the homotopy perturbation method, which is a combination of the classical perturbation technique and homotopy concept as used in topology. In the homotopy perturbation method, which requires neither a small parameter nor a linear term in a differential equation, a homotopy with an embedding parameter p ∈ [0, 1] is constructed. In [1] a basic idea of homotopy perturbation method for solving nonlinear differential equations was presented. A numerous nonlinear problems were recently treated by the method. We in the present paper investigate the homotopy perturbation technique from a mathematical point of view. The aim is to analyze the method and to show that under certain circumstances, by particular choice of auxiliary linear operator and initial approximation, the homotopy perturbation method simply