New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals
In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs) in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The said...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2016-09-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016816301855 |
| _version_ | 1819200013929021440 |
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| author | Liaqat Ali Saeed Islam Taza Gul Ilyas Khan L.C.C. Dennis |
| author_facet | Liaqat Ali Saeed Islam Taza Gul Ilyas Khan L.C.C. Dennis |
| author_sort | Liaqat Ali |
| collection | DOAJ |
| description | In this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs) in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4) and Optimal Homotopy Asymptotic Method (OHAM-1). The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective. |
| first_indexed | 2024-12-23T03:25:29Z |
| format | Article |
| id | doaj.art-ecf8dcc8e5fd4e01aad5bda1f03b512a |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-23T03:25:29Z |
| publishDate | 2016-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-ecf8dcc8e5fd4e01aad5bda1f03b512a2022-12-21T18:01:52ZengElsevierAlexandria Engineering Journal1110-01682016-09-015532811281910.1016/j.aej.2016.07.013New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervalsLiaqat Ali0Saeed Islam1Taza Gul2Ilyas Khan3L.C.C. Dennis4Department of Mathematics, Abdul Wali Khan University Mardan KPK, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan KPK, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan KPK, PakistanCollege of Engineering, Majmaah University, Majmaah, Saudi ArabiaDepartment of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, 31750 Perak, MalaysiaIn this research work a new version of Optimal Homotopy Asymptotic Method is applied to solve nonlinear boundary value problems (BVPs) in finite and infinite intervals. It comprises of initial guess, auxiliary functions (containing unknown convergence controlling parameters) and a homotopy. The said method is applied to solve nonlinear Riccati equations and nonlinear BVP of order two for thin film flow of a third grade fluid on a moving belt. It is also used to solve nonlinear BVP of order three achieved by Mostafa et al. for Hydro-magnetic boundary layer and micro-polar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. The obtained results are compared with the existing results of Runge-Kutta (RK-4) and Optimal Homotopy Asymptotic Method (OHAM-1). The outcomes achieved by this method are in excellent concurrence with the exact solution and hence it is proved that this method is easy and effective.http://www.sciencedirect.com/science/article/pii/S1110016816301855Initial guessAuxiliary parametersAuxiliary functionsGalerkin’s methodEmbedding parameterOptimal Homotopy Asymptotic MethodNew version of Optimal Homotopy Asymptotic Method |
| spellingShingle | Liaqat Ali Saeed Islam Taza Gul Ilyas Khan L.C.C. Dennis New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals Alexandria Engineering Journal Initial guess Auxiliary parameters Auxiliary functions Galerkin’s method Embedding parameter Optimal Homotopy Asymptotic Method New version of Optimal Homotopy Asymptotic Method |
| title | New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals |
| title_full | New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals |
| title_fullStr | New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals |
| title_full_unstemmed | New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals |
| title_short | New version of Optimal Homotopy Asymptotic Method for the solution of nonlinear boundary value problems in finite and infinite intervals |
| title_sort | new version of optimal homotopy asymptotic method for the solution of nonlinear boundary value problems in finite and infinite intervals |
| topic | Initial guess Auxiliary parameters Auxiliary functions Galerkin’s method Embedding parameter Optimal Homotopy Asymptotic Method New version of Optimal Homotopy Asymptotic Method |
| url | http://www.sciencedirect.com/science/article/pii/S1110016816301855 |
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