Solutions of Emden–Fowler equations by homotopy-perturbation methods
In this paper, approximate and/or exact analytical solutions of the generalized Emden–Fowler type equations in the second-order ordinary differential equations (ODEs) are obtained by homotopy-perturbation method (HPM). The homotopy-perturbation method (HPM) is a coupling of the perturbation method a...
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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/6656/ http://irep.iium.edu.my/6656/1/Solutions_of_Emden%E2%80%93Fowler_equations_by_homotopy-perturbation_method.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, approximate and/or exact analytical solutions of the generalized Emden–Fowler type equations in the second-order ordinary differential equations (ODEs) are obtained by homotopy-perturbation method (HPM). The homotopy-perturbation method (HPM) is a coupling of the perturbation method and the homotopy method. The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. In this work, HPM yields solutions in convergent series forms with easily computable terms, and in some cases, only one iteration leads to the high accuracy of the solutions. Comparisons with the exact solutions and the solutions obtained by the Adomian decomposition method (ADM) show the efficiency of HPM in solving equations with singularity. |
| first_indexed | 2025-11-14T14:34:22Z |
| format | Article |
| id | iium-6656 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:34:22Z |
| publishDate | 2009 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-66562011-11-24T03:45:26Z http://irep.iium.edu.my/6656/ Solutions of Emden–Fowler equations by homotopy-perturbation methods Chowdhury, Md. Sazzad Hossien Hashim, Ishak QA76 Computer software In this paper, approximate and/or exact analytical solutions of the generalized Emden–Fowler type equations in the second-order ordinary differential equations (ODEs) are obtained by homotopy-perturbation method (HPM). The homotopy-perturbation method (HPM) is a coupling of the perturbation method and the homotopy method. The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve. In this work, HPM yields solutions in convergent series forms with easily computable terms, and in some cases, only one iteration leads to the high accuracy of the solutions. Comparisons with the exact solutions and the solutions obtained by the Adomian decomposition method (ADM) show the efficiency of HPM in solving equations with singularity. Elsevier 2009-02 Article PeerReviewed application/pdf en http://irep.iium.edu.my/6656/1/Solutions_of_Emden%E2%80%93Fowler_equations_by_homotopy-perturbation_method.pdf Chowdhury, Md. Sazzad Hossien and Hashim, Ishak (2009) Solutions of Emden–Fowler equations by homotopy-perturbation methods. Nonlinear Analysis: Real World Applications, 10 (1). pp. 104-115. ISSN 1468-1218 http://www.sciencedirect.com/science/article/pii/S1468121807001599 doi:10.1016/j.nonrwa.2007.08.017 |
| spellingShingle | QA76 Computer software Chowdhury, Md. Sazzad Hossien Hashim, Ishak Solutions of Emden–Fowler equations by homotopy-perturbation methods |
| title | Solutions of Emden–Fowler equations by homotopy-perturbation
methods |
| title_full | Solutions of Emden–Fowler equations by homotopy-perturbation
methods |
| title_fullStr | Solutions of Emden–Fowler equations by homotopy-perturbation
methods |
| title_full_unstemmed | Solutions of Emden–Fowler equations by homotopy-perturbation
methods |
| title_short | Solutions of Emden–Fowler equations by homotopy-perturbation
methods |
| title_sort | solutions of emden–fowler equations by homotopy-perturbation
methods |
| topic | QA76 Computer software |
| url | http://irep.iium.edu.my/6656/ http://irep.iium.edu.my/6656/ http://irep.iium.edu.my/6656/ http://irep.iium.edu.my/6656/1/Solutions_of_Emden%E2%80%93Fowler_equations_by_homotopy-perturbation_method.pdf |