A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them i...
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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/10.1155/2013/423628 |
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| _version_ | 1832545278270373888 |
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| author | S. S. Motsa |
| author_facet | S. S. Motsa |
| author_sort | S. S. Motsa |
| collection | DOAJ |
| description | We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM), is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques. |
| format | Article |
| id | doaj-art-05db47d49d4f416daae0dd863048f36e |
| 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-05db47d49d4f416daae0dd863048f36e2025-02-03T07:26:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/423628423628A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow ProblemsS. S. Motsa0School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South AfricaWe propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM), is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.http://dx.doi.org/10.1155/2013/423628 |
| spellingShingle | S. S. Motsa A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems Journal of Applied Mathematics |
| title | A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems |
| title_full | A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems |
| title_fullStr | A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems |
| title_full_unstemmed | A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems |
| title_short | A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems |
| title_sort | new spectral local linearization method for nonlinear boundary layer flow problems |
| url | http://dx.doi.org/10.1155/2013/423628 |
| work_keys_str_mv | AT ssmotsa anewspectrallocallinearizationmethodfornonlinearboundarylayerflowproblems AT ssmotsa newspectrallocallinearizationmethodfornonlinearboundarylayerflowproblems |