A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations
Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures availabl...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/105414 |
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| author | Mazhar Iqbal M. T. Mustafa Azad A. Siddiqui |
| author_facet | Mazhar Iqbal M. T. Mustafa Azad A. Siddiqui |
| author_sort | Mazhar Iqbal |
| collection | DOAJ |
| description | Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium. |
| format | Article |
| id | doaj-art-0fd2b4f4609b46ee8aa7bee7e5aeaefd |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0fd2b4f4609b46ee8aa7bee7e5aeaefd2025-08-20T03:54:29ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/105414105414A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential EquationsMazhar Iqbal0M. T. Mustafa1Azad A. Siddiqui2Department of Basic Sciences and Humanities, EME College, National University of Sciences and Technology (NUST), Peshawar Road, Rawalpindi 46000, PakistanDepartment of Mathematics, Statistics and Physics, Qatar University, P.O. Box 2713, Doha, QatarSchool of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, PakistanStandard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium.http://dx.doi.org/10.1155/2014/105414 |
| spellingShingle | Mazhar Iqbal M. T. Mustafa Azad A. Siddiqui A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations Abstract and Applied Analysis |
| title | A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations |
| title_full | A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations |
| title_fullStr | A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations |
| title_full_unstemmed | A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations |
| title_short | A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations |
| title_sort | method for generating approximate similarity solutions of nonlinear partial differential equations |
| url | http://dx.doi.org/10.1155/2014/105414 |
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