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Izv. IMI UdGU, 2021, Volume 57, Pages 128–141 (Mi iimi412)  

MATHEMATICS

Crank-Nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay

M. Ibrahim, V. G. Pimenov

Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620000, Russia

Abstract: A two-dimensional in space fractional diffusion equation with functional delay of a general form is considered. For this problem, the Crank-Nicolson method is constructed, based on shifted Grunwald-Letnikov formulas for approximating fractional derivatives with respect to each spatial variable and using piecewise linear interpolation of discrete history with continuation extrapolation to take into account the delay effect. The Douglas scheme is used to reduce the emerging high-dimensional system to tridiagonal systems. The residual of the method is investigated. To obtain the order of the method, we reduce the systems to constructions of the general difference scheme with heredity. A theorem on the second order of convergence of the method in time and space steps is proved. The results of numerical experiments are presented.

Keywords: diffusion equation, two spatial coordinates, functional delay, Grunwald-Letnikov approximation, Crank-Nicolson method, factorization, order of convergence.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00019
The study of the second author was funded by RFBR, project number 19-01-00019.


DOI: https://doi.org/10.35634/2226-3594-2021-57-05

Full text: PDF file (162 kB)
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Bibliographic databases:

UDC: 519.63
MSC: 65M06, 65M12, 65M15, 65Q20
Received: 04.03.2021
Language:

Citation: 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

Citation in format AMSBIB
\Bibitem{IbrPim21}
\by M.~Ibrahim, V.~G.~Pimenov
\paper Crank-Nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay
\jour Izv. IMI UdGU
\yr 2021
\vol 57
\pages 128--141
\mathnet{http://mi.mathnet.ru/iimi412}
\crossref{https://doi.org/10.35634/2226-3594-2021-57-05}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000661445200005}


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