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Differential-Difference Equations with Optimal Parameters

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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.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. F. Mastryukov

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  1. A. F. Mastryukov
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Correspondence to A. F. Mastryukov.

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Translated by E. Chernokozhin

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Mastryukov, A.F. Differential-Difference Equations with Optimal Parameters. Comput. Math. and Math. Phys. 63, 2060–2068 (2023). https://doi.org/10.1134/S0965542523110155

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  • DOI: https://doi.org/10.1134/S0965542523110155

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