Apekov A.M., Beshtokov M.K., Beshtokova Z.V., Shomakhov Z.V. MPCS author guidelines
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https://doi.org/10.15688/mpcm.jvolsu.2020.4.4
Aslan M. Apekov
Candidate of Physical and Mathematical Sciences, Department Of Computational
methods,
Institute of applied mathematics and automation, Kabardino-Balkarian scientific center
of RAS
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https://orcid.org/0000-0002-6269-3717
Shortanova ul. 89A, 360000, Nalchik, Russian Federation
Murat K. Beshtokov
Candidate of Physical and Mathematical Sciences, Associate Professor, Department of
Computational methods,
Institute of applied mathematics and automation, Kabardino-Balkarian scientific center
of RAS
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https://orcid.org/0000-0003-2968-9211
Shortanova ul. 89A, 360000, Nalchik, Russian Federation
Zaryana V. Beshtokova
Associate Professor, Department of Computational methods,
Institute of applied mathematics and automation, Kabardino-Balkarian scientific center
of RAS
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Shortanova ul. 89A, 360000, Nalchik, Russian Federation
Zamir V. Shomakhov
Candidate of Physical and Mathematical Sciences, Associate Professor, Department of
Computational methods,
Institute of applied mathematics and automation, Kabardino-Balkarian scientific center
of RAS
This email address is being protected from spambots. You need JavaScript enabled to view it.
https://orcid.org/0000-0001-5738-2626
Shortanova ul. 89A, 360000, Nalchik, Russian Federation
Abstract. In a rectangular domain the first and third initial-boundary value problems are studied for the one-dimensional with respect to the spatial variable diffusion convection equation with a fractional Caputo derivative and a nonlocal linear source of integral form. Using the method of energy inequalities, under the assumption of the existence of a regular solution, a priori estimates are obtained in differential form, which implies the uniqueness and continuous dependence of the solution on the input data of the problem.
On a uniform grid, two difference schemes are constructed that approximate the first and third initial-boundary value problems, respectively. For the solution of the difference problems, a priori estimates are obtained in the difference interpretation. The obtained estimates in difference form imply uniqueness and stability, as well as convergence at a rate equal to the order of the approximation error.
An algorithm for the approximate solution of the third boundary value problem is constructed, numerical calculations of test examples are carried out, illustrating the theoretical results obtained in this work.
Key words: initial boundary value problems, a priori estimation, convectiondiffusion equation, fractional order differential equation, fractional Caputo derivative.
MPCS author guidelines by Apekov A.M., Beshtokov M.K., Beshtokova Z.V., Shomakhov Z.V. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 23 No. 4 2020, pp. 35-50
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