New Iterative Method for Solving the Fornberg-Whitham Equation and Comparison with Homotopy Perturbation Transform Method

Abstract

This paper presents an approximate analytical solution of the nonlinear Fornberg-Whitham equation using the new iterative method (NIM). A comparison is made between the NIM results, homotopy perturbation transform method (HPTM) and the Adomian's decomposition method (ADM). The solution procedure reveals that NIM is a reliable, simple and effective. The proposed technique solves nonlinear problems without using Adomian's polynomials and He's polynomials which is a clear advantage of it over the decomposition method. The results reveal that the proposed algorithm is very efficient, simple and can be applied to other nonlinear problems.