A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations
We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters α and β. In addition, the problem is reduced...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/760542 |
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| author | E. H. Doha D. Baleanu A. H. Bhrawy M. A. Abdelkawy |
| author_facet | E. H. Doha D. Baleanu A. H. Bhrawy M. A. Abdelkawy |
| author_sort | E. H. Doha |
| collection | DOAJ |
| description | We solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters α and β. In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations. |
| format | Article |
| id | doaj-art-da980a2c21ab4fd8bbe8775e2900bdb7 |
| 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-da980a2c21ab4fd8bbe8775e2900bdb72025-02-03T01:03:29ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/760542760542A Jacobi Collocation Method for Solving Nonlinear Burgers-Type EquationsE. H. Doha0D. Baleanu1A. H. Bhrawy2M. A. Abdelkawy3Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, EgyptWe solve three versions of nonlinear time-dependent Burgers-type equations. The Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters α and β. In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high-accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers-type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.http://dx.doi.org/10.1155/2013/760542 |
| spellingShingle | E. H. Doha D. Baleanu A. H. Bhrawy M. A. Abdelkawy A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations Abstract and Applied Analysis |
| title | A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations |
| title_full | A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations |
| title_fullStr | A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations |
| title_full_unstemmed | A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations |
| title_short | A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations |
| title_sort | jacobi collocation method for solving nonlinear burgers type equations |
| url | http://dx.doi.org/10.1155/2013/760542 |
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