This article is cited in 2 papers

General numerical methods

Difference scheme for the numerical solution of the Burgers equation

V. V. Markov^a, V. N. Utesinov<sup>b

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991 Russia
^b Kostyakov All-Russia Research Institute for Hydraulic Engineering and Land Reclamation, Moscow, 127550 Russia

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.

Key words: Burgers equation, difference scheme, stability condition for difference scheme.

UDC: 519.63

Received: 25.02.2020
Revised: 25.02.2020
Accepted: 04.08.2020

DOI: 10.31857/S0044466920120108

 English version: Computational Mathematics and Mathematical Physics, 2020, 60:12, 1985–1989

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