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Difference Scheme for the Numerical Solution of the Burgers Equation

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Abstract

A second-order accurate finite-difference scheme based on existing methods is proposed for the numerical solution of the one-dimensional Burgers equation. A stability condition is given under which the integration time step does not depend on the value of the viscous term. The numerical results produced by the scheme are compared with the exact solution of the Burgers equation.

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Funding

This study was performed at the Steklov Mathematical Institute of the Russian Academy of Sciences and was supported by the Russian Science Foundation, project no. 19-71-30012.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    V. V. Markov

  2. Kostyakov All-Russia Research Institute for Hydraulic Engineering and Land Reclamation, 127550, Moscow, Russia

    V. N. Utesinov

Authors
  1. V. V. Markov
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  2. V. N. Utesinov
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Corresponding author

Correspondence to V. N. Utesinov.

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Translated by I. Ruzanova

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Markov, V.V., Utesinov, V.N. Difference Scheme for the Numerical Solution of the Burgers Equation. Comput. Math. and Math. Phys. 60, 1985–1989 (2020). https://doi.org/10.1134/S0965542520120106

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  • DOI: https://doi.org/10.1134/S0965542520120106

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