Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method
The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30188/ http://psasir.upm.edu.my/id/eprint/30188/1/30188.pdf |
| _version_ | 1848846606639562752 |
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| author | Atangana, Abdon Kilicman, Adem |
| author_facet | Atangana, Abdon Kilicman, Adem |
| author_sort | Atangana, Abdon |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as N tends to infinity. |
| first_indexed | 2025-11-15T09:05:23Z |
| format | Article |
| id | upm-30188 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:23Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301882016-03-31T08:24:46Z http://psasir.upm.edu.my/id/eprint/30188/ Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method Atangana, Abdon Kilicman, Adem The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as N tends to infinity. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30188/1/30188.pdf Atangana, Abdon and Kilicman, Adem (2013) Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method. Abstract and Applied Analysis, 2013. art. no. 380484. pp. 1-9. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2013/380484/abs/ 10.1155/2013/380484 |
| spellingShingle | Atangana, Abdon Kilicman, Adem Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method |
| title | Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method |
| title_full | Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method |
| title_fullStr | Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method |
| title_full_unstemmed | Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method |
| title_short | Analytical solutions of boundary values problem of 2D and 3D Poisson and biharmonic equations by homotopy decomposition method |
| title_sort | analytical solutions of boundary values problem of 2d and 3d poisson and biharmonic equations by homotopy decomposition method |
| url | http://psasir.upm.edu.my/id/eprint/30188/ http://psasir.upm.edu.my/id/eprint/30188/ http://psasir.upm.edu.my/id/eprint/30188/ http://psasir.upm.edu.my/id/eprint/30188/1/30188.pdf |