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A Finite-Difference Scheme for the One-Dimensional Maxwell Equations

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ABSTRACT

This paper deals with a difference scheme of second-order approximation using Laquerre transform for the one-dimensional Maxwell equations. Supplementary parameters are introduced into this difference scheme. These parameters are obtained by minimizing the error of a difference approximation for a Helmholtz equation. The optimal parameters do not depend on the step size and the number of nodes in the difference scheme. It is shown that the use of the Laguerre decomposition method allows obtaining higher accuracy of approximation of the equations in comparison with similar difference schemes when using the Fourier decomposition method. The second-order finite difference scheme with the parameters is compared to a fourth-order difference scheme in two cases: The use of the optimal difference scheme when solving a problem of electromagnetic pulse propagation in an inhomogeneous medium yields a solution accuracy comparable to that obtained with the fourth-order difference scheme. When solving an inverse problem the second-order difference scheme allows obtaining higher solution accuracy as compared to the fourth-order difference scheme. In these problems the second-order difference scheme with the supplementary parameters has decreased the calculation time by 20–25% as compared to the fourth-order difference scheme.

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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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Mastryukov, A.F. A Finite-Difference Scheme for the One-Dimensional Maxwell Equations. Numer. Analys. Appl. 13, 57–67 (2020). https://doi.org/10.1134/S199542392001005X

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  • DOI: https://doi.org/10.1134/S199542392001005X

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