Homotopy Perturbation Method with an Auxiliary Term

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...

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Main Author: Ji-Huan He
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/857612
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author Ji-Huan He
author_facet Ji-Huan He
author_sort Ji-Huan He
collection DOAJ
description 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.
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institution Kabale University
issn 1085-3375
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series Abstract and Applied Analysis
spelling doaj-art-d67a923a50494a9f9cccb3a391608a232025-02-03T05:51:48ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/857612857612Homotopy Perturbation Method with an Auxiliary TermJi-Huan He0National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, ChinaThe 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.http://dx.doi.org/10.1155/2012/857612
spellingShingle Ji-Huan He
Homotopy Perturbation Method with an Auxiliary Term
Abstract and Applied Analysis
title Homotopy Perturbation Method with an Auxiliary Term
title_full Homotopy Perturbation Method with an Auxiliary Term
title_fullStr Homotopy Perturbation Method with an Auxiliary Term
title_full_unstemmed Homotopy Perturbation Method with an Auxiliary Term
title_short Homotopy Perturbation Method with an Auxiliary Term
title_sort homotopy perturbation method with an auxiliary term
url http://dx.doi.org/10.1155/2012/857612
work_keys_str_mv AT jihuanhe homotopyperturbationmethodwithanauxiliaryterm