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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 7, Pages 1082–1100
DOI: https://doi.org/10.31857/S0044466921070024 (Mi zvmmf11260) 		 
Partial Differential Equations

Local one-dimensional scheme for the first initial-boundary value problem for the multidimensional fractional-order convection–diffusion equation

A. A. Alikhanova, M. KH. Beshtokovb, M. H. Shhanukov-Lafishevb

a North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355017, Stavropol, Russia
b Institute of Applied Mathematics and Automation, Kabardin-Balkar Science Center, Russian Academy of Sciences, 360004, Nalchik, Russia
DOI: https://doi.org/10.31857/S0044466921070024
Abstract: The first boundary value problem for the fractional-order convection–diffusion equation is studied. A locally one-dimensional difference scheme is constructed. Using the maximum principle, a prior estimate is obtained in the uniform metric. The stability and convergence of the difference scheme are proved. An algorithm for the approximate solution of a locally one-dimensional difference scheme is constructed. Numerical calculations illustrating the theoretical results obtained in the work are performed.
Key words: partial differential equation, convection–diffusion equation, fractional-order derivative, fractional time derivative in the Caputo sense, locally one-dimensional difference scheme, stability and convergence of difference schemes.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-53007
This work was supported by the Russian Foundation for Basic Research, project no. 20-51-53007.
Received: 14.09.2020
Revised: 26.11.2020
Accepted: 11.03.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 7, Pages 1075–1093
DOI: https://doi.org/10.1134/S0965542521070022
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: A. A. Alikhanov, M. KH. Beshtokov, M. H. Shhanukov-Lafishev, “Local one-dimensional scheme for the first initial-boundary value problem for the multidimensional fractional-order convection–diffusion equation”, Zh. Vychisl. Mat. Mat. Fiz., 61:7 (2021), 1082–1100; Comput. Math. Math. Phys., 61:7 (2021), 1075–1093
Citation in format AMSBIB
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\paper Local one-dimensional scheme for the first initial-boundary value problem for the multidimensional fractional-order convection–diffusion equation
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\yr 2021
\vol 61
\issue 7
\pages 1082--1100
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\crossref{https://doi.org/10.31857/S0044466921070024}
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