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Title: | Numerical method for solving an initial-boundary value problem for a multidimensional loaded parabolic equation of a general form with conditions of the third kind |
Authors: | Beshtokova, Z. V. Бештокова, З. В. |
Keywords: | Parabolic equation;Multidi- mensional problem;Loaded equation;Difference schemes;Locally one-dimensional scheme;A priori estimate;Stability;Convergence |
Issue Date: | 2022 |
Publisher: | Samara State Technical University |
Citation: | Beshtokova, Z. V. Numerical method for solving an initial-boundary value problem for a multidimensional loaded parabolic equation of a general form with conditions of the third kind // Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta-seriya-fiziko-matematicheskiye Nauki. - 2022. - vol. 26. - no. 1. - pp. 7–35. - DOI10.14498/vsgtu1908 |
Series/Report no.: | Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta-seriya-fiziko-matematicheskiye Nauki |
Abstract: | An initial-boundary value problem is studied for a multidimensional loaded parabolic equation of general form with boundary conditions of the third kind. For a numerical solution, a locally one-dimensional difference scheme by A.A. Samarskii with order of approximation O(h2+t) is constructed. Using the method of energy inequalities, we obtain a priori estimates in the differential and difference interpretations, which imply unique- ness, stability, and convergence of the solution of the locally one-dimensional difference scheme to the solution of the original differential problem in the L2 norm at a rate equal to the order of approximation of the difference scheme. An algorithm for the computational solution is constructed and numerical calculations of test cases are carried out, illustrating the theoretical calculations obtained in this work. |
URI: | http://hdl.handle.net/20.500.12258/19601 |
Appears in Collections: | Статьи, проиндексированные в SCOPUS, WOS |
Files in This Item:
File | Description | Size | Format | |
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WoS 1402 .pdf Restricted Access | 1.06 MB | Adobe PDF | View/Open | |
scopusresults 2213 .pdf Restricted Access | 66.66 kB | Adobe PDF | View/Open |
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