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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 11, Pages 1839–1848
DOI: https://doi.org/10.31857/S0044466923110224
(Mi zvmmf11648)
 

Ordinary differential equations

Differential-difference equations with optimal parameters

A. F. Mastryukov

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
Abstract: The paper considers difference schemes with optimal parameters for solving Maxwell’s equations. Using Laguerre transforms, the numerical values of the optimal parameters are determined and differential-difference equations are constructed. Differential-difference equations are solved by the finite-difference method with iterations over small optimal parameters. Optimal second-order difference schemes for one-dimensional and two-dimensional Maxwell’s equations are considered. Optimal parameters of difference schemes are given. It is shown that the use of optimal difference schemes leads to an increase in the accuracy of solution.
Key words: differential-difference equations, finite-difference method, optimal, accuracy, electromagnetic waves, Laguerre method.
Received: 16.12.2022
Revised: 13.06.2023
Accepted: 25.07.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 40, Issue 11, Pages 2060–2068
DOI: https://doi.org/10.1134/S0965542523110155
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: A. F. Mastryukov, “Differential-difference equations with optimal parameters”, Zh. Vychisl. Mat. Mat. Fiz., 63:11 (2023), 1839–1848; Comput. Math. Math. Phys., 40:11 (2023), 2060–2068
Citation in format AMSBIB
\Bibitem{Mas23}
\by A.~F.~Mastryukov
\paper Differential-difference equations with optimal parameters
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 11
\pages 1839--1848
\mathnet{http://mi.mathnet.ru/zvmmf11648}
\crossref{https://doi.org/10.31857/S0044466923110224}
\elib{https://elibrary.ru/item.asp?id=54720591}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 40
\issue 11
\pages 2060--2068
\crossref{https://doi.org/10.1134/S0965542523110155}
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