Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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 Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.]: Year: Volume: Issue: Page: Find

 Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2020, Issue 3, Pages 27–40 (Mi vtpmk560)

Mathematical Modelling, Numerical Methods and Software Systems

A grid method for solving the first initial boundary value problem for a loaded differential equation of fractional order convection diffusion

M. KH. Beshtokov

Institute of Applied Mathematics and Automation, Nalchik

Abstract: The first initial boundary value problem for a loaded differential equation of fractional order convection diffusion is considered. A difference scheme approximating this problem is constructed on a uniform grid. To solve the problem, assuming the existence of a regular solution, a priori estimates in differential and difference forms are obtained. From these estimates follow the uniqueness and continuous dependence of the solution on the input data of the problem, as well as the convergence with the rate $O(h^2+\tau^2)$.

Keywords: loaded equations, boundary value problems, a priori estimation, convection diffusion equation, fractional order differential equation, fractional Caputo derivative.

DOI: https://doi.org/10.26456/vtpmk560

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UDC: 519.63
MSC: 35K05
Revised: 02.10.2020

Citation: M. KH. Beshtokov, “A grid method for solving the first initial boundary value problem for a loaded differential equation of fractional order convection diffusion”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2020, no. 3, 27–40

Citation in format AMSBIB
\Bibitem{Bes20} \by M.~KH.~Beshtokov \paper A grid method for solving the first initial boundary value problem for a loaded differential equation of fractional order convection diffusion \jour Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.] \yr 2020 \issue 3 \pages 27--40 \mathnet{http://mi.mathnet.ru/vtpmk560} \crossref{https://doi.org/10.26456/vtpmk560} \elib{https://elibrary.ru/item.asp?id=44503274}