The homotopy analysis method for solving the Fornberg-Whitham equation and comparison with Adomian's decomposition method

Authors:
Fayçal Abidi;Khaled Omrani
Affiliations:
Ecole Polytechnique de Tunis, Rue El Khawarezmi, 2078 La Marsa, Tunisia;Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, 4003 Sousse Ibn Khaldoun, Tunisia
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this work, an analytical technique, namely the homotopy analysis method (HAM), is applied to obtain an approximate analytical solution of the Fornberg-Whitham equation. A comparison is made between the HAM results and the Adomian's decomposition method (ADM) and the homotopy perturbation method (HPM). The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series.