The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations
We introduce two powerful methods to solve the generalized Zakharov equations; one is the homotopy perturbation method and the other is the homotopy analysis method. The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/561252 |
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| author | Hassan A. Zedan Eman El Adrous |
| author_facet | Hassan A. Zedan Eman El Adrous |
| author_sort | Hassan A. Zedan |
| collection | DOAJ |
| description | We introduce two powerful methods to solve the generalized Zakharov equations; one is the homotopy perturbation method and the other is the homotopy analysis method. The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions; the homotopy analysis method is applied to solve the generalized Zakharov equations. HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZE equations and the approximate solutions, comparison of the HPM results with those of Adomian’s decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZE equations with the HPM solutions and HAM solutions are presented. |
| format | Article |
| id | doaj-art-915ac125f0cf44519a6fb3d1d5f5898e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-915ac125f0cf44519a6fb3d1d5f5898e2025-02-03T01:03:32ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/561252561252The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov EquationsHassan A. Zedan0Eman El Adrous1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe introduce two powerful methods to solve the generalized Zakharov equations; one is the homotopy perturbation method and the other is the homotopy analysis method. The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions; the homotopy analysis method is applied to solve the generalized Zakharov equations. HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZE equations and the approximate solutions, comparison of the HPM results with those of Adomian’s decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZE equations with the HPM solutions and HAM solutions are presented.http://dx.doi.org/10.1155/2012/561252 |
| spellingShingle | Hassan A. Zedan Eman El Adrous The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations Abstract and Applied Analysis |
| title | The Application of the Homotopy Perturbation Method and the
Homotopy Analysis Method to the Generalized Zakharov Equations |
| title_full | The Application of the Homotopy Perturbation Method and the
Homotopy Analysis Method to the Generalized Zakharov Equations |
| title_fullStr | The Application of the Homotopy Perturbation Method and the
Homotopy Analysis Method to the Generalized Zakharov Equations |
| title_full_unstemmed | The Application of the Homotopy Perturbation Method and the
Homotopy Analysis Method to the Generalized Zakharov Equations |
| title_short | The Application of the Homotopy Perturbation Method and the
Homotopy Analysis Method to the Generalized Zakharov Equations |
| title_sort | application of the homotopy perturbation method and the homotopy analysis method to the generalized zakharov equations |
| url | http://dx.doi.org/10.1155/2012/561252 |
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