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Skew-Symmetric Difference Analogs of the Fourth-Order Approximation to the First Derivative

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Abstract

Assume that we have an initial–boundary value problem for a system of first-order hyperbolic equations that has an integral conservation law. One of the options for the numerical solution of this kind of a problem is the construction of a difference scheme for spatial variables, followed by the solution of the resulting system of ordinary differential equations. For the stability of the solution of this ODE system, it is desirable that it has a first integral that is an analog of the conservation law for the original problem. An antisymmetric difference analog of the first derivative of the fourth-order approximation is constructed for this purpose.

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Funding

The work was carried out within the framework of the state order for the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    V. V. Skazka

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    V. V. Skazka

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  1. V. V. Skazka
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Correspondence to V. V. Skazka.

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Translated by V. Potapchouck

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Skazka, V.V. Skew-Symmetric Difference Analogs of the Fourth-Order Approximation to the First Derivative. J. Appl. Ind. Math. 16, 789–799 (2022). https://doi.org/10.1134/S1990478922040184

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  • DOI: https://doi.org/10.1134/S1990478922040184

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