Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer
The medium through which the groundwater moves varies in time and space. The Hantush equation describes the movement of groundwater through a leaky aquifer. To include explicitly the deformation of the leaky aquifer into the mathematical formulation, we modify the equation by replacing the partial d...
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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/10.1155/2013/691060 |
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| author | Abdon Atangana S. C. Oukouomi Noutchie |
| author_facet | Abdon Atangana S. C. Oukouomi Noutchie |
| author_sort | Abdon Atangana |
| collection | DOAJ |
| description | The medium through which the groundwater moves varies in time and space. The Hantush equation describes the movement of groundwater through a leaky aquifer. To include explicitly the deformation of the leaky aquifer into the mathematical formulation, we modify the equation by replacing the partial derivative with respect to time by the time-fractional variable order derivative. The modified equation is solved numerically via the Crank-Nicolson scheme. The stability and the convergence in this case are presented in details. |
| format | Article |
| id | doaj-art-3608928c5370445689e6eda81a2cef2a |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3608928c5370445689e6eda81a2cef2a2025-08-20T02:08:15ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/691060691060Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable AquiferAbdon Atangana0S. C. Oukouomi Noutchie1Institute for Groundwater Studies, University of the Free State, P.O. Box 399, Bloemfontein, South AfricaDepartment of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South AfricaThe medium through which the groundwater moves varies in time and space. The Hantush equation describes the movement of groundwater through a leaky aquifer. To include explicitly the deformation of the leaky aquifer into the mathematical formulation, we modify the equation by replacing the partial derivative with respect to time by the time-fractional variable order derivative. The modified equation is solved numerically via the Crank-Nicolson scheme. The stability and the convergence in this case are presented in details.http://dx.doi.org/10.1155/2013/691060 |
| spellingShingle | Abdon Atangana S. C. Oukouomi Noutchie Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer Abstract and Applied Analysis |
| title | Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer |
| title_full | Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer |
| title_fullStr | Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer |
| title_full_unstemmed | Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer |
| title_short | Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer |
| title_sort | stability and convergence of a time fractional variable order hantush equation for a deformable aquifer |
| url | http://dx.doi.org/10.1155/2013/691060 |
| work_keys_str_mv | AT abdonatangana stabilityandconvergenceofatimefractionalvariableorderhantushequationforadeformableaquifer AT scoukouominoutchie stabilityandconvergenceofatimefractionalvariableorderhantushequationforadeformableaquifer |