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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
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11648 https://www.mathnet.ru/eng/zvmmf/v63/i11/p1839
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