Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM) is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on...

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Main Authors: M. S. H. Chowdhury, I. Hashim, S. Momani, M. M. Rahman
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/974293
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spelling doaj-1544622e11514c2ab8c2c179f03844a32020-11-24T20:44:47ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/974293974293Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio SystemM. S. H. Chowdhury0I. Hashim1S. Momani2M. M. Rahman3Deptartment of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, 53100 Kuala Lumpur, MalaysiaSchool of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, MalaysiaDepartment of Mathematics, The University of Jordan, Amman 11942, JordanDepartment of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 Selangor, MalaysiaFinding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM) is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM). The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4) solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.http://dx.doi.org/10.1155/2012/974293
collection DOAJ
language English
format Article
sources DOAJ
author M. S. H. Chowdhury
I. Hashim
S. Momani
M. M. Rahman
spellingShingle M. S. H. Chowdhury
I. Hashim
S. Momani
M. M. Rahman
Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
Abstract and Applied Analysis
author_facet M. S. H. Chowdhury
I. Hashim
S. Momani
M. M. Rahman
author_sort M. S. H. Chowdhury
title Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
title_short Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
title_full Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
title_fullStr Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
title_full_unstemmed Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
title_sort application of multistage homotopy perturbation method to the chaotic genesio system
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM) is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM). The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4) solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.
url http://dx.doi.org/10.1155/2012/974293
work_keys_str_mv AT mshchowdhury applicationofmultistagehomotopyperturbationmethodtothechaoticgenesiosystem
AT ihashim applicationofmultistagehomotopyperturbationmethodtothechaoticgenesiosystem
AT smomani applicationofmultistagehomotopyperturbationmethodtothechaoticgenesiosystem
AT mmrahman applicationofmultistagehomotopyperturbationmethodtothechaoticgenesiosystem
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