Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes
A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this...
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| Main Authors: | , |
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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/10.1155/2013/828764 |
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| _version_ | 1832545343450906624 |
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| author | Abdon Atangana Dumitru Baleanu |
| author_facet | Abdon Atangana Dumitru Baleanu |
| author_sort | Abdon Atangana |
| collection | DOAJ |
| description | A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions. |
| format | Article |
| id | doaj-art-f4a7b7c22aca48e698d23a71c39aea90 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f4a7b7c22aca48e698d23a71c39aea902025-02-03T07:26:11ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/828764828764Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference SchemesAbdon Atangana0Dumitru Baleanu1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South AfricaDepartment of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi ArabiaA kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.http://dx.doi.org/10.1155/2013/828764 |
| spellingShingle | Abdon Atangana Dumitru Baleanu Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes Abstract and Applied Analysis |
| title | Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes |
| title_full | Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes |
| title_fullStr | Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes |
| title_full_unstemmed | Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes |
| title_short | Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes |
| title_sort | numerical solution of a kind of fractional parabolic equations via two difference schemes |
| url | http://dx.doi.org/10.1155/2013/828764 |
| work_keys_str_mv | AT abdonatangana numericalsolutionofakindoffractionalparabolicequationsviatwodifferenceschemes AT dumitrubaleanu numericalsolutionofakindoffractionalparabolicequationsviatwodifferenceschemes |