On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows
This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms...
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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/10.1155/2014/848170 |
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| author | S. S. Motsa |
| author_facet | S. S. Motsa |
| author_sort | S. S. Motsa |
| collection | DOAJ |
| description | This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. The applicability and effectiveness of the expanded SHAM approach are tested on a non-linear PDE that models the problem of unsteady boundary layer flow caused by an impulsively stretching plate. Numerical simulations are conducted to generate results for the important flow properties such as the local skin friction. The accuracy of the present results is validated against existing results from the literature and against results generated using the Keller-box method. The preliminary results from the proposed study indicate that the present method is more accurate and computationally efficient than more traditional methods used for solving PDEs that describe nonsimilar boundary layer flow. |
| format | Article |
| id | doaj-art-7d74a7fe0b7646c9b023b86653db499d |
| 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-7d74a7fe0b7646c9b023b86653db499d2025-02-03T06:01:10ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/848170848170On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer FlowsS. S. Motsa0School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South AfricaThis work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. The applicability and effectiveness of the expanded SHAM approach are tested on a non-linear PDE that models the problem of unsteady boundary layer flow caused by an impulsively stretching plate. Numerical simulations are conducted to generate results for the important flow properties such as the local skin friction. The accuracy of the present results is validated against existing results from the literature and against results generated using the Keller-box method. The preliminary results from the proposed study indicate that the present method is more accurate and computationally efficient than more traditional methods used for solving PDEs that describe nonsimilar boundary layer flow.http://dx.doi.org/10.1155/2014/848170 |
| spellingShingle | S. S. Motsa On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows Abstract and Applied Analysis |
| title | On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows |
| title_full | On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows |
| title_fullStr | On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows |
| title_full_unstemmed | On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows |
| title_short | On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows |
| title_sort | on an interpolation based spectral homotopy analysis method for pde based unsteady boundary layer flows |
| url | http://dx.doi.org/10.1155/2014/848170 |
| work_keys_str_mv | AT ssmotsa onaninterpolationbasedspectralhomotopyanalysismethodforpdebasedunsteadyboundarylayerflows |