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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 12, Pages 2050–2054 (Mi zvmmf10990)  

General numerical methods

Difference scheme for the numerical solution of the Burgers equation

V. V. Markova, V. N. Utesinovb

a 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.

Funding Agency Grant Number
Russian Science Foundation 19-71-30012
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.


DOI: https://doi.org/10.31857/S0044466920120108


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

Bibliographic databases:

UDC: 519.63
Received: 25.02.2020
Revised: 25.02.2020
Accepted:04.08.2020

Citation: V. V. Markov, V. N. Utesinov, “Difference scheme for the numerical solution of the Burgers equation”, Zh. Vychisl. Mat. Mat. Fiz., 60:12 (2020), 2050–2054; Comput. Math. Math. Phys., 60:12 (2020), 1985–1989

Citation in format AMSBIB
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