Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method.
In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usua...
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| Format: | Article |
| Language: | English English |
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INSInet Publication
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25088/ http://psasir.upm.edu.my/id/eprint/25088/1/Exact%20solution%20for%20linear%20and%20nonlinear%20systems%20of%20PDEs%20by%20Homotopy.pdf |
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| author | Chowdhury, M.S.H. Hashim, I. Ismail, A.F. Rahman, Md. Mahmudur Momani, S. |
| author_facet | Chowdhury, M.S.H. Hashim, I. Ismail, A.F. Rahman, Md. Mahmudur Momani, S. |
| author_sort | Chowdhury, M.S.H. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of 'deformations', the solution of each of which is 'close' to that at the previous stage of 'deformation'. Eventually at p = 1, the system takes the original form of the equation and the final stage of 'deformation' gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method. |
| first_indexed | 2025-11-15T08:43:15Z |
| format | Article |
| id | upm-25088 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:43:15Z |
| publishDate | 2011 |
| publisher | INSInet Publication |
| recordtype | eprints |
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| spelling | upm-250882015-10-06T03:48:48Z http://psasir.upm.edu.my/id/eprint/25088/ Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. Chowdhury, M.S.H. Hashim, I. Ismail, A.F. Rahman, Md. Mahmudur Momani, S. In this paper, the homotopy-perturbation method (HPM) proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of 'deformations', the solution of each of which is 'close' to that at the previous stage of 'deformation'. Eventually at p = 1, the system takes the original form of the equation and the final stage of 'deformation' gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method. INSInet Publication 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/25088/1/Exact%20solution%20for%20linear%20and%20nonlinear%20systems%20of%20PDEs%20by%20Homotopy.pdf Chowdhury, M.S.H. and Hashim, I. and Ismail, A.F. and Rahman, Md. Mahmudur and Momani, S. (2011) Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. Australian Journal of Basic and Applied Sciences, 5 (12). pp. 3295-3305. ISSN 1991-8178 http://www.ansinet.com/ English |
| spellingShingle | Chowdhury, M.S.H. Hashim, I. Ismail, A.F. Rahman, Md. Mahmudur Momani, S. Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. |
| title | Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. |
| title_full | Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. |
| title_fullStr | Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. |
| title_full_unstemmed | Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. |
| title_short | Exact solution for linear and nonlinear systems of PDEs by Homotopy-Perturbation method. |
| title_sort | exact solution for linear and nonlinear systems of pdes by homotopy-perturbation method. |
| url | http://psasir.upm.edu.my/id/eprint/25088/ http://psasir.upm.edu.my/id/eprint/25088/ http://psasir.upm.edu.my/id/eprint/25088/1/Exact%20solution%20for%20linear%20and%20nonlinear%20systems%20of%20PDEs%20by%20Homotopy.pdf |