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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 8, Pages 1437–1444
DOI: https://doi.org/10.31857/S0044466924080084 (Mi zvmmf11811) 		 
General numerical methods

An approach to improving the accuracy and efficiency of the ROMB method for solving the nonstationary heat equation

N. Ya. Moiseev

Russian Federal Nuclear Center–Zababakhin All-Russia Research Institute of Technical Physics, 456770, Snezhinsk, Chelyabinsk oblast, Russia
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DOI: https://doi.org/10.31857/S0044466924080084
Abstract: A modification of the ROMB method for the numerical solution of nonstationary nonlinear heat equations is presented. The modified difference schemes are conservative and, on smooth solutions, provide a second-order approximation in time and space for model differential equations with constant coefficients. For the modified difference schemes, the first differential approximations are given, which make it possible to estimate the truncation errors of the schemes.
Key words: nonstationary nonlinear heat equation, predictor–corrector difference schemes, ROMB method.
Received: 02.04.2024
Revised: 02.04.2024
Accepted: 05.05.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 8, Pages 1747–1754
DOI: https://doi.org/10.1134/S096554252470088X
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: N. Ya. Moiseev, “An approach to improving the accuracy and efficiency of the ROMB method for solving the nonstationary heat equation”, Zh. Vychisl. Mat. Mat. Fiz., 64:8 (2024), 1437–1444; Comput. Math. Math. Phys., 64:8 (2024), 1747–1754
Citation in format AMSBIB
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\paper An approach to improving the accuracy and efficiency of the ROMB method for solving the nonstationary heat equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 8
\pages 1437--1444
\mathnet{http://mi.mathnet.ru/zvmmf11811}
\crossref{https://doi.org/10.31857/S0044466924080084}
\elib{https://elibrary.ru/item.asp?id=75224106}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 8
\pages 1747--1754
\crossref{https://doi.org/10.1134/S096554252470088X}
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