New Iterative Method for Solving the Fornberg-Whitham Equation and Comparison with Homotopy Perturbation Transform Method
Mohamed A. Ramadan *
Department of Mathematics, Faculty of Science, Menoufia University, Egypt.
Mohamed S. Al-luhaibi
Department of Mathematics, Faculty of Science, Kirkuk University, Iraq.
*Author to whom correspondence should be addressed.
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.
Keywords: New iterative method, Homotopy perturbation transform method, Nonlinear Fornberg-Whitham equation.