O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 796–815; Comput. Math. Math. Phys., 56:5 (2016), 783

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 5, Pages 796–815
DOI: https://doi.org/10.7868/S0044466916050124 (Mi zvmmf10388)

This article is cited in 8 scientific papers (total in 8 papers)

Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field

O. A. Kovyrkina^ab, V. V. Ostapenko^ab

^a Novosibirsk State University, Universitetskii pr. 2, Novosibirsk, 630090, Russia
^b Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent'eva 15, Novosibirsk, 630090, Russia

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DOI: https://doi.org/10.7868/S0044466916050124

Abstract: The monotonicity of the CABARET scheme approximating a hyperbolic differential equation with a sign-changing characteristic field is analyzed. Monotonicity conditions for this scheme are obtained in domains where the characteristics have a sign-definite propagation velocity and near sonic lines, on which the propagation velocity changes its sign. These properties of the CABARET scheme are illustrated by test computations.

Key words: CABARET difference scheme, hyperbolic equations, sign-changing characteristic field, monotonicity.

Received: 08.07.2015
Revised: 19.10.2015

English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 5, Pages 783–801
DOI: https://doi.org/10.1134/S0965542516050122

Bibliographic databases:

Document Type: Article

UDC: 519.633

Language: Russian

Citation: O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 796–815; Comput. Math. Math. Phys., 56:5 (2016), 783–801

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This publication is cited in the following 8 articles:

M. D. Bragin, O. A. Kovyrkina, M. E. Ladonkina, V. V. Ostapenko, V. F. Tishkin, N. A. Khandeeva, “Combined numerical schemes”, Comput. Math. Math. Phys., 62:11 (2022), 1743–1781
V. V. Ostapenko, V. A. Kolotilov, “Primenenie skhemy CABARET dlya rascheta razryvnykh reshenii giperbolicheskoi sistemy zakonov sokhraneniya”, Dokl. RAN. Matem., inform., prots. upr., 501 (2021), 62–66
N. A. Zyuzina, V. V. Ostapenko, E. I. Polunina, “Splitting method for CABARET scheme approximating the non-uniform scalar conservation law”, Num. Anal. Appl., 11:2 (2018), 146–157
V. V. Ostapenko, “On strong monotonicity of two-layer in time CABARET scheme”, Math. Models Comput. Simul., 11:1 (2019), 1–8
N. A. Zyuzina, O. A. Kovyrkina, V. V. Ostapenko, “On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field”, Math. Models Comput. Simul., 11:1 (2019), 46–60
N. A. Zyuzina, V. V. Ostapenko, “Decay of unstable strong discontinuities in the case of a convex-flux scalar conservation law approximated by the CABARET scheme”, Comput. Math. Math. Phys., 58:6 (2018), 950–966
O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws”, Comput. Math. Math. Phys., 58:9 (2018), 1435–1450
Efremov A., Karepova E., Shaydurov V., Vyatkin A., “Semi-Lagrangian method for advection problem with adaptive grid”, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS?16 (Albena, Bulgaria, 22?27 June 2016), AIP Conference Proceedings, 1773, ed. Todorov M., Amer Inst Physics, 2016, 100003

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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