vmaitComputational Mathematics and Information TechnologiesComputational Mathematics and Information Technologies2587-8999Донской государственный технический университет10.23947/2587-8999-2018-2-1-44-59vmait-68Research ArticleСтатьиАдаптивный модифицированный попеременно-треугольный методAdaptive modified alternating-triangular methodhttps://orcid.org/0000-0002-5875-1523СухиновАлександр ИвановичSukhinovAlexander Ivanovich

Сухинов Александр Иванович, Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1), доктор физико-математических наук, профессор

Sukhinov Alexander Ivanovich, Don State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths, Professor

sukhinov@gmail.comhttps://orcid.org/0000-0002-8323-6005ЧистяковАлександр ЕвгеньевичChistyakovAlexander Evgenievich

Чистяков Александр Евгеньевич, Донской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1), доктор физико-математических наук, доцент

Chistyakov Alexander Evgenievich, Don State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation), Doctor of Science in Physics and Maths, Associate professor

cheese_05@mail.ruДонской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1)РоссияDon State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation)Russian FederationДонской государственный технический университет (344000 Ростов-на-Дону, пл. Гагарина, д. 1)РоссияDon State Technical University (1st Gagarin Square, Rostov-on-Don, Russian Federation)Russian Federation2018280320232168Copyright © Сухинов А.И., Чистяков А.Е., 20232023Сухинов А.И., Чистяков А.Е.Sukhinov A.I., Chistyakov A.E.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.cmit-journal.ru/jour/article/view/68

Работа посвящена разработке адаптивных методов для решения задач конвекции-диффузии. Для данного класса задач построен вариант адаптивного модифицированного попеременно–треугольного метода минимальных поправок и аналитически получены оценки скорости сходимости для данного метода.

The paper covers the development of adaptive methods for solving convection-diffusion problems. For this class of problems a version of minimal correction adaptive modified alternating-triangular method was developed, as well the convergence rate of the method was analytically estimated. Numerical results have been presented for solving real hydrodynamical problem in shallow water using parallel algorithm of developed method.

сеточные уравнения с несамосопряженным операторомадаптивный попеременно-треугольный методпараллельные алгоритмы решения сеточных уравненийwave problemgrid equationsadaptive modified alternating triangular iterative methodThe research is done with the financial support from the RSF, Projects No. 17-11-01286.ReferencesSamarskiy A.A. Teoriya raznostnykh skhem. M. Nauka, 1989.Samarskiy A.A. Teoriya raznostnykh skhem. M. Nauka, 1989.Konovalov A.N. K teorii poperemenno - treugol'nogo iteratsionnogo metoda // Sibirskiy matematicheskiy zhurnal, 2002, 43:3, – pp. 552-572.Konovalov A.N. K teorii poperemenno - treugol'nogo iteratsionnogo metoda // Sibirskiy matematicheskiy zhurnal, 2002, 43:3, – pp. 552-572.Samarskiy A.A., Vabishchevich P.N. Chislennyye metody resheniya zadach konvektsii-diffuzii. M., Editorial URSS, 1999.Samarskiy A.A., Vabishchevich P.N. Chislennyye metody resheniya zadach konvektsii-diffuzii. M., Editorial URSS, 1999.Samarskiy A.A., Nikolayev Ye.S. 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The authors declare that there are no conflicts of interest present.