An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs
In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/259371 |
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| author | Eman S. Alaidarous Malik Zaka Ullah Fayyaz Ahmad A.S. Al-Fhaid |
| author_facet | Eman S. Alaidarous Malik Zaka Ullah Fayyaz Ahmad A.S. Al-Fhaid |
| author_sort | Eman S. Alaidarous |
| collection | DOAJ |
| description | In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013). The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations. |
| format | Article |
| id | doaj-art-1ab94a5169ef47329dd1d8d4f895aa75 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1ab94a5169ef47329dd1d8d4f895aa752025-02-03T01:02:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/259371259371An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPsEman S. Alaidarous0Malik Zaka Ullah1Fayyaz Ahmad2A.S. Al-Fhaid3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartamento de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Compte d’Urgell 187, 08036 Barcelona, SpainDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaIn this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013). The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.http://dx.doi.org/10.1155/2013/259371 |
| spellingShingle | Eman S. Alaidarous Malik Zaka Ullah Fayyaz Ahmad A.S. Al-Fhaid An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs Journal of Applied Mathematics |
| title | An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs |
| title_full | An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs |
| title_fullStr | An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs |
| title_full_unstemmed | An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs |
| title_short | An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs |
| title_sort | efficient higher order quasilinearization method for solving nonlinear bvps |
| url | http://dx.doi.org/10.1155/2013/259371 |
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