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.
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.
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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
\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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This publication is cited in the following 11 articles:
A. A. Issakhov, A. B. Abylkassymova, R. E. Zhailybaev, S. L. Yun, “STABILITY CONDITION OF FINITE DIFFERENCE SCHEMES FOR PARABOLIC AND HYPERBOLIC EQUATIONS: A COMPARISON WITH FINITE VOLUME METHODS FOR FRACTIONAL-ORDER DIFFUSION”, jour, 22:1 (2025), 184
V. G. Pimenov, A. B. Lozhnikov, “Asimptoticheskoe razlozhenie pogreshnosti chislennogo metoda dlya resheniya superdiffuzionnogo uravneniya s funktsionalnym zapazdyvaniem”, Tr. IMM UrO RAN, 30, no. 2, 2024, 138–151
V. G. Pimenov, A. V. Lekomtsev, “Kompaktnaya skhema dlya resheniya superdiffuzionnogo uravneniyas neskolkimi peremennymi zapazdyvaniyami”, Vestnik rossiiskikh universitetov. Matematika, 29:148 (2024), 440–454
M. Ibrahim, V. G. Pimenov, “Crank-Nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay”, Izv. IMI UdGU, 57 (2021), 128–141
M. Kh. Beshtokov, F. A. Erzhibova, “On Boundary Value Problems for Fractional-Order Differential Equations”, Sib. Adv. Math., 31:4 (2021), 229
Tursun K. Yuldashev, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 020016
M. Kh. Beshtokov, F. A. Erzhibova, “K kraevym zadacham dlya integro-differentsialnykh uravnenii drobnogo poryadka”, Matem. tr., 23:1 (2020), 16–36
M. Kh. Beshtokov, “Kraevye zadachi dlya nagruzhennogo modifitsirovannogo uravneniya vlagoperenosa drobnogo poryadka s operatorom Besselya i raznostnye metody ikh resheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:2 (2020), 158–175
Svyatoslav Solodushkin, Tatiana Gorbova, Vladimir Pimenov, Springer Proceedings in Mathematics & Statistics, 333, Differential and Difference Equations with Applications, 2020, 689
Vladimir Pimenov, Ahmed Hendy, Mohammad Ibrahim, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2312, PROCEEDINGS OF THE X ALL-RUSSIAN CONFERENCE “Actual Problems of Applied Mathematics and Mechanics” with International Participation, Dedicated to the Memory of Academician A.F. Sidorov and 100th Anniversary of UrFU: AFSID-2020, 2020, 050017
Irina Iumanova, Svyatoslav Solodushkin, Springer Proceedings in Mathematics & Statistics, 333, Differential and Difference Equations with Applications, 2020, 373
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