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


Sakar M. G. , Erdoğan F.

APPLIED MATHEMATICAL MODELLING, vol.37, pp.8876-8885, 2013 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37
  • Publication Date: 2013
  • Doi Number: 10.1016/j.apm.2013.03.074
  • Journal Name: APPLIED MATHEMATICAL MODELLING
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.8876-8885
  • Keywords: Homotopy analysis method, Time-fractional Fornberg-Whitham equation, Caputo derivative, Adomian's decompositon method, Auxiliary parameter, PARTIAL-DIFFERENTIAL-EQUATIONS, NUMERICAL-METHODS, APPROXIMATE

Abstract

In this paper, we applied relatively new analytical techniques, the homotopy analysis method (HAM) and the Adomian’s decomposition method (ADM) for solving time-fractional Fornberg–Whitham equation. The homotopy analysis method contains the auxiliary parameter, which provides us with a simple way to adjust and control the convergence region of solution series. The fractional derivatives are described in the Caputo sense. A comparison is made the between HAM and ADM results. The present methods performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of the problem are presented.

In this paper, we applied relatively new analytical techniques, the homotopy analysis method (HAM) and the Adomian's decomposition method (ADM) for solving time-fractional Fomberg-Whitham equation. The homotopy analysis method contains the auxiliary parameter, which provides us with a simple way to adjust and control the convergence region of solution series. The fractional derivatives are described in the Caputo sense. A comparison is made the between HAM and ADM results. The present methods performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of the problem are presented. (C) 2013 Elsevier Inc. All rights reserved.