Abstract and Applied Analysis
Volume 2012 (2012), Article ID 857612, 7 pages
http://dx.doi.org/10.1155/2012/857612
Research Article

Homotopy Perturbation Method with an Auxiliary Term

Ji-Huan He1,2

1National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, China
2Modern Textile Institute, Donghua University, Shanghai 200051, China

Received 2 October 2011; Accepted 17 November 2011

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Ji-Huan He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution procedure.