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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 86–90 (Mi into172)  

This article is cited in 4 scientific papers (total in 4 papers)

Numerical method for fractional advection-diffusion equation with heredity

V. G. Pimenovab

a Institute of Mathematics and Mechanics, Ural Branch of the AS of USSR
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (278 kB) Citations (4)
Abstract: We propose a method of construction of difference schemes for fractional partial differential equations with delay in time. For the fractional equation with two-sided diffusion, fractional transfer in time, and a functional aftereffect, we construct an imokicit difference scheme. We use the shifted Grünwald–Letnikov formulas for the approximation of fractional derivatives with respect to spatial variables and the $L1$-algorithm for the approximation of fractional derivatives in time. Also we use the piecewise constant interpolation and extrapolation by extending of the discrete prehistory of model in time. The algorithm is a fractional analog of a purely implicit method; on each time step, it is reduced to the solution of linear algebraic systems. We prove the stability of the method and find its order of convergence.
Keywords: equation with fractional derivatives, functional delay, mesh scheme, interpolation, extrapolation, order of convergence.
Funding agency Grant number
Russian Science Foundation 14-35-00005
Ministry of Education and Science of the Russian Federation 02.À03.21.0006 îò 27.08.2013
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 737–741
DOI: https://doi.org/10.1007/s10958-018-3780-6
Bibliographic databases:
Document Type: Article
UDC: 519.63
MSC: 65N12
Language: Russian
Citation: V. G. Pimenov, “Numerical method for fractional advection-diffusion equation with heredity”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 86–90; J. Math. Sci. (N. Y.), 230:5 (2018), 737–741
Citation in format AMSBIB
\Bibitem{Pim17}
\by V.~G.~Pimenov
\paper Numerical method for fractional advection-diffusion equation with heredity
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 86--90
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into172}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801392}
\zmath{https://zbmath.org/?q=an:1395.65053}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 737--741
\crossref{https://doi.org/10.1007/s10958-018-3780-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044443385}
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  • This publication is cited in the following 4 articles:
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