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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 8, Pages 1272–1278
DOI: https://doi.org/10.31857/S0044466923080136 (Mi zvmmf11597) 		 
General numerical methods

An improved difference scheme for the Cauchy problem in the case of a transport equation

G. I. Shishkin, L. P. Shishkina

Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, 620108, Yekaterinburg, Russia
DOI: https://doi.org/10.31857/S0044466923080136
Abstract: The Cauchy problem for the regular transport equation is considered. The Richardson technique is used to construct an improved difference scheme that converges in the maximum norm with the second order of convergence.
Key words: transport equation, Cauchy problem, standard difference scheme, uniform grid, residual, expansion of residual, monotonicity of differential and grid problems, Richardson technique, improved difference scheme, convergence in the maximum norm.
Received: 04.04.2023
Revised: 04.04.2023
Accepted: 28.04.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 8, Pages 1401–1407
DOI: https://doi.org/10.1134/S0965542523080134
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: G. I. Shishkin, L. P. Shishkina, “An improved difference scheme for the Cauchy problem in the case of a transport equation”, Zh. Vychisl. Mat. Mat. Fiz., 63:8 (2023), 1272–1278; Comput. Math. Math. Phys., 63:8 (2023), 1401–1407
Citation in format AMSBIB
\Bibitem{ShiShi23}
\by G.~I.~Shishkin, L.~P.~Shishkina
\paper An improved difference scheme for the Cauchy problem in the case of a transport equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 8
\pages 1272--1278
\mathnet{http://mi.mathnet.ru/zvmmf11597}
\crossref{https://doi.org/10.31857/S0044466923080136}
\elib{https://elibrary.ru/item.asp?id=54270655}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 8
\pages 1401--1407
\crossref{https://doi.org/10.1134/S0965542523080134}
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