A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY
For two sided space fractional diffusion equation with time functional after-effect, an implicit numerical method is constructed and the order of its convergence is obtained. The method is a fractional analogue of the Crank–Nicholson method, and also uses interpolation and extrapolation of the prehi...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2016-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/38 |
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| author | Vladimir G. Pimenov Ahmed S. Hendy |
| author_facet | Vladimir G. Pimenov Ahmed S. Hendy |
| author_sort | Vladimir G. Pimenov |
| collection | DOAJ |
| description | For two sided space fractional diffusion equation with time functional after-effect, an implicit numerical method is constructed and the order of its convergence is obtained. The method is a fractional analogue of the Crank–Nicholson method, and also uses interpolation and extrapolation of the prehistory of model with respect to time. |
| format | Article |
| id | doaj-art-0b5b2c0f7f9f4073ac0242303203ad51 |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2016-07-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-0b5b2c0f7f9f4073ac0242303203ad512025-08-20T02:41:48ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522016-07-012110.15826/umj.2016.1.00513A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAYVladimir G. Pimenov0Ahmed S. Hendy1Ural Federal University; Krasovskii Institute of Mathematics and Mechanics, EkaterinburgUral Federal University, EkaterinburgFor two sided space fractional diffusion equation with time functional after-effect, an implicit numerical method is constructed and the order of its convergence is obtained. The method is a fractional analogue of the Crank–Nicholson method, and also uses interpolation and extrapolation of the prehistory of model with respect to time.https://umjuran.ru/index.php/umj/article/view/38Fractional partial differential equation, Grunwald-Letnikov approximations, Grid schemes, Functional delay, Interpolation, Extrapolation, Convergence order |
| spellingShingle | Vladimir G. Pimenov Ahmed S. Hendy A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY Ural Mathematical Journal Fractional partial differential equation, Grunwald-Letnikov approximations, Grid schemes, Functional delay, Interpolation, Extrapolation, Convergence order |
| title | A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY |
| title_full | A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY |
| title_fullStr | A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY |
| title_full_unstemmed | A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY |
| title_short | A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY |
| title_sort | fractional analog of crank nicholson method for the two sided space fractional partial equation with functional delay |
| topic | Fractional partial differential equation, Grunwald-Letnikov approximations, Grid schemes, Functional delay, Interpolation, Extrapolation, Convergence order |
| url | https://umjuran.ru/index.php/umj/article/view/38 |
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