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Ural Mathematical Journal, 2016, Volume 2, Issue 1, Pages 48–57
DOI: https://doi.org/10.15826/umj.2016.1.005 (Mi umj14) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay

Vladimir G. Pimenovab, Ahmed S. Hendyb

a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Department of Computational Mathematics, Ural Federal University, Ekaterinburg, Russia
Full-text PDF (178 kB) Citations (9)
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DOI: https://doi.org/10.15826/umj.2016.1.005
Abstract: 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.
Keywords: Fractional partial differential equation, Grunwald-Letnikov approximations, Grid schemes, Functional delay, Interpolation, Extrapolation, Convergence order.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
Russian Science Foundation 14-35-00005
This work was supported by Government of the Russian Federation program 02.A03.21.0006 on 27.08.2013 and by Russian Science Foundation 14-35-00005.
Bibliographic databases:
Document Type: Article
Language: English
Citation: Vladimir G. Pimenov, Ahmed S. Hendy, “Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay”, Ural Math. J., 2:1 (2016), 48–57
Citation in format AMSBIB
\Bibitem{PimHen16}
\by Vladimir~G.~Pimenov, Ahmed~S.~Hendy
\paper Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay
\jour Ural Math. J.
\yr 2016
\vol 2
\issue 1
\pages 48--57
\mathnet{http://mi.mathnet.ru/umj14}
\crossref{https://doi.org/10.15826/umj.2016.1.005}
\zmath{https://zbmath.org/?q=an:1398.65217}
\elib{https://elibrary.ru/item.asp?id=26501482}
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