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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/380484 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832565179497316352 |
|---|---|
| author | Abdon Atangana Adem Kılıçman |
| author_facet | Abdon Atangana Adem Kılıçman |
| author_sort | Abdon Atangana |
| collection | DOAJ |
| 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 tends to infinity. |
| format | Article |
| id | doaj-art-90d49e7ad31c4d27a9ff3d5beded4b51 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-90d49e7ad31c4d27a9ff3d5beded4b512025-02-03T01:09:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/380484380484Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition MethodAbdon Atangana0Adem Kılıçman1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South AfricaDepartment of Mathematics and Institute for Mathematical Research, University of Putra Malaysia, 43400 Serdang, Selangor, MalaysiaThe 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 tends to infinity.http://dx.doi.org/10.1155/2013/380484 |
| spellingShingle | Abdon Atangana Adem Kılıçman Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method Abstract and Applied Analysis |
| 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://dx.doi.org/10.1155/2013/380484 |
| work_keys_str_mv | AT abdonatangana analyticalsolutionsofboundaryvaluesproblemof2dand3dpoissonandbiharmonicequationsbyhomotopydecompositionmethod AT ademkılıcman analyticalsolutionsofboundaryvaluesproblemof2dand3dpoissonandbiharmonicequationsbyhomotopydecompositionmethod |