Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102810
Title: Crank-nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay
Authors: Mohammad, I.
Germanovich, P. V.
Issue Date: 2021
Publisher: Udmurt State University
Citation: Mohammad I. Crank-nicolson scheme for two-dimensional in space fractional diffusion equations with functional delay / I. Mohammad, P. V. Germanovich. — DOI 10.35634/2226-3594-2021-57-05 // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta. — 2021. — Vol. 57. — P. 128-141.
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. © 2021 Udmurt State University. All rights reserved.
Keywords: CRANK-NICOLSON METHOD
DIFFUSION EQUATION
FACTORIZATION
FUNCTIONAL DELAY
GRUNWALD-LETNIKOV APPROXIMATION
ORDER OF CONVERGENCE
TWO SPATIAL COORDINATES
URI: http://hdl.handle.net/10995/102810
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85108969553
PURE ID: 22130757
ISSN: 22263594
DOI: 10.35634/2226-3594-2021-57-05
metadata.dc.description.sponsorship: The study of the second author was funded by RFBR, project number 19–01–00019.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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