Beshtokov M.K., Vodakhova V.A., Isakova M.M. Approximate Solution of the First Boundary Value Problem for the Loaded Heat Conduction Equation
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https://doi.org/10.15688/mpcm.jvolsu.2023.3.1
Murat Kh. Beshtokov
Candidate of Sciences (Physics and Mathematics), Associate Professor, Leading Researcher, Department of Computational Methods, Institute of Applied Mathematics and Automation,
Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
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,
https://orcid.org/0000-0003-2968-9211
Shortanova St, 89A, 360000 Nalchik, Russian Federation
Valentina A. Vodakhova
Candidate of Sciences (Physics and Mathematics), Associate Professor, Department of Algebra and Differential Equations, Institute of Physics and Mathematics,
Kabardino-Balkarian State University named after Kh.M. Berbekov
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,
https://orcid.org/0009-0001-9990-7467
Chernyshevskogo St, 173, 360004 Nalchik, Russian Federation
Mariana M. Isakova
Candidate of Sciences (Physics and Mathematics), Associate Professor, Department of Algebra and Differential Equations, Institute of Physics and Mathematics,
Kabardino-Balkarian State University named after Kh.M. Berbekov
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,
https://orcid.org/0000-0003-1189-9456
Chernyshevskogo St, 173, 360004 Nalchik, Russian Federation
Abstract. The first boundary value problem for the loaded heat equation with variable coefficients is studied. For the numerical solution of the problem posed, a difference scheme of a high order of accuracy is constructed. An a priori estimate in difference form is obtained by the method of energy inequalities. This estimate implies the uniqueness and stability of the solution with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the original differential problem at a rate of O(h4 + t2). An algorithm for the approximate solution is constructed, and numerical calculations of test examples are carried out, illustrating the theoretical results obtained in the work.
Key words: first boundary value problem, loaded equation, heat equation, difference scheme, a priori estimate, stability and convergence.
On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Nonlinear Ordinary Differential Fourth Order Equation by Beshtokov M.K., Vodakhova V.A., Isakova M.M. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 26 No. 4 2023, pp. 5-17
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