A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation
We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville formula. We prove that the CE-SE approximation is conditionally stable unde...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/303857 |
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| _version_ | 1832556976036380672 |
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| author | Silvia Jerez Ivan Dzib |
| author_facet | Silvia Jerez Ivan Dzib |
| author_sort | Silvia Jerez |
| collection | DOAJ |
| description | We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for
the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville
formula. We prove that the CE-SE approximation is conditionally stable under
mild requirements. A numerical simulation is
performed for the one-dimensional case by considering a benchmark with a discontinuous initial condition
in order to compare the results with the analytical solution. |
| format | Article |
| id | doaj-art-b68889818c8a42d8a2ebda440e0f7389 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b68889818c8a42d8a2ebda440e0f73892025-02-03T05:43:59ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/303857303857A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion EquationSilvia Jerez0Ivan Dzib1Department of Applied Mathematics, CIMAT, Jalisco s/n, 36240 Guanajuato, GTO, MexicoDepartment of Applied Mathematics, CIMAT, Jalisco s/n, 36240 Guanajuato, GTO, MexicoWe obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville formula. We prove that the CE-SE approximation is conditionally stable under mild requirements. A numerical simulation is performed for the one-dimensional case by considering a benchmark with a discontinuous initial condition in order to compare the results with the analytical solution.http://dx.doi.org/10.1155/2015/303857 |
| spellingShingle | Silvia Jerez Ivan Dzib A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation Discrete Dynamics in Nature and Society |
| title | A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation |
| title_full | A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation |
| title_fullStr | A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation |
| title_full_unstemmed | A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation |
| title_short | A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation |
| title_sort | discrete method based on the ce se formulation for the fractional advection dispersion equation |
| url | http://dx.doi.org/10.1155/2015/303857 |
| work_keys_str_mv | AT silviajerez adiscretemethodbasedontheceseformulationforthefractionaladvectiondispersionequation AT ivandzib adiscretemethodbasedontheceseformulationforthefractionaladvectiondispersionequation AT silviajerez discretemethodbasedontheceseformulationforthefractionaladvectiondispersionequation AT ivandzib discretemethodbasedontheceseformulationforthefractionaladvectiondispersionequation |