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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Main Authors: Vladimir G. Pimenov, Ahmed S. Hendy
Format: Article
Language:English
Published: 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
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.
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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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