On some modified variational iteration methods for solving the one-dimensional sine–Gordon equation

Abstract

In this paper, we present modified variational iteration methods (MVIM) to solve the sine–Gordon equation which play a very important part in applied and engineering sciences. Two versions of MVIM are made by the classical variational iteration method coupled with other methods such as homotopy perturbation method and Adomian decomposition method (ADM). The reliability and efficiency of the proposed methods are discussed and illustrated by numerical examples. Moreover, it has the advantage of higher precision and is easier to implement when compared with the ADM.

Keywords:

• sine–Gordon equation
• Adomian polynomials
• He's polynomials
• homotopy perturbation methods
• modified variational iteration method

2000 AMS Subject Classifications :

• 37K10
• 35Q53
• 78M30
• 76M30
• 65M99

Acknowledgements

The authors express their great thanks to referees for the valuable advices. The present work was supported by National Basic Research Program under the Grant 2005CB32170X.