Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations
A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite...
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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/10.1155/2014/757204 |
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| author | B. A. Jacobs C. Harley |
| author_facet | B. A. Jacobs C. Harley |
| author_sort | B. A. Jacobs |
| collection | DOAJ |
| description | A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time. |
| format | Article |
| id | doaj-art-c60a510ea3024e20b533d962150537b0 |
| 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-c60a510ea3024e20b533d962150537b02025-02-03T01:26:08ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/757204757204Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential EquationsB. A. Jacobs0C. Harley1Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South AfricaCentre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South AfricaA computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.http://dx.doi.org/10.1155/2014/757204 |
| spellingShingle | B. A. Jacobs C. Harley Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations Abstract and Applied Analysis |
| title | Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations |
| title_full | Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations |
| title_fullStr | Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations |
| title_full_unstemmed | Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations |
| title_short | Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations |
| title_sort | two hybrid methods for solving two dimensional linear time fractional partial differential equations |
| url | http://dx.doi.org/10.1155/2014/757204 |
| work_keys_str_mv | AT bajacobs twohybridmethodsforsolvingtwodimensionallineartimefractionalpartialdifferentialequations AT charley twohybridmethodsforsolvingtwodimensionallineartimefractionalpartialdifferentialequations |