Application of multistage homotopy-perturbation method for the solutions of the Chen system
In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The HPM is treated as an algorithm in a sequence of intervals for finding accurat...
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| Format: | Article |
| Language: | English |
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Elsevier
2009
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| Online Access: | http://irep.iium.edu.my/6643/ http://irep.iium.edu.my/6643/1/Application_of_multistage_homotopy-perturbation_method_for_the_solutions_of_the_Chen_system.pdf |
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| author | Chowdhury, Md. Sazzad Hossien Hashim, Ishak |
| author_facet | Chowdhury, Md. Sazzad Hossien Hashim, Ishak |
| author_sort | Chowdhury, Md. Sazzad Hossien |
| building | IIUM Repository |
| collection | Online Access |
| description | In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chen system.We shall call this technique as the multistage
HPM (for short MHPM). In particular we look at the accuracy of the HPM as the Chen system changes from a nonchaotic system to a chaotic one. Numerical comparisons between the MHPM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear chaotic and nonchaotic systems of ODEs. |
| first_indexed | 2025-11-14T14:34:19Z |
| format | Article |
| id | iium-6643 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:34:19Z |
| publishDate | 2009 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-66432011-11-24T06:40:07Z http://irep.iium.edu.my/6643/ Application of multistage homotopy-perturbation method for the solutions of the Chen system Chowdhury, Md. Sazzad Hossien Hashim, Ishak QA76 Computer software In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chen system.We shall call this technique as the multistage HPM (for short MHPM). In particular we look at the accuracy of the HPM as the Chen system changes from a nonchaotic system to a chaotic one. Numerical comparisons between the MHPM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear chaotic and nonchaotic systems of ODEs. Elsevier 2009 Article PeerReviewed application/pdf en http://irep.iium.edu.my/6643/1/Application_of_multistage_homotopy-perturbation_method_for_the_solutions_of_the_Chen_system.pdf Chowdhury, Md. Sazzad Hossien and Hashim, Ishak (2009) Application of multistage homotopy-perturbation method for the solutions of the Chen system. Nonlinear Analysis: Real World Applications, 10 (1). pp. 381-391. ISSN 1468-1218 http://www.sciencedirect.com/science/article/pii/S1468121807001848 doi:10.1016/j.nonrwa.2007.09.014 |
| spellingShingle | QA76 Computer software Chowdhury, Md. Sazzad Hossien Hashim, Ishak Application of multistage homotopy-perturbation method for the solutions of the Chen system |
| title | Application of multistage homotopy-perturbation method for the solutions of the Chen system |
| title_full | Application of multistage homotopy-perturbation method for the solutions of the Chen system |
| title_fullStr | Application of multistage homotopy-perturbation method for the solutions of the Chen system |
| title_full_unstemmed | Application of multistage homotopy-perturbation method for the solutions of the Chen system |
| title_short | Application of multistage homotopy-perturbation method for the solutions of the Chen system |
| title_sort | application of multistage homotopy-perturbation method for the solutions of the chen system |
| topic | QA76 Computer software |
| url | http://irep.iium.edu.my/6643/ http://irep.iium.edu.my/6643/ http://irep.iium.edu.my/6643/ http://irep.iium.edu.my/6643/1/Application_of_multistage_homotopy-perturbation_method_for_the_solutions_of_the_Chen_system.pdf |