Ya. A. Kholodov, A. S. Kholodov, I. V. Tsybulin, “Construction of monotone difference schemes for systems of hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 30–49; Comput. Math. Math. Phys., 58:8 (2018), 1226

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 8, Pages 30–49
DOI: https://doi.org/10.31857/S004446690001999-9 (Mi zvmmf10760)

This article is cited in 10 scientific papers (total in 10 papers)

Construction of monotone difference schemes for systems of hyperbolic equations

Ya. A. Kholodov^ab, A. S. Kholodov^ca, I. V. Tsybulin^c

^a Institute of Computer Aided Design, Russian Academy of Sciences, Moscow, Russia
^b Innopolis University, Innopolis, Russia
^c Moscow Institute of Physics and Technology, Dolgoprudny, Russia

Citations (10)

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DOI: https://doi.org/10.31857/S004446690001999-9

Abstract: A distinctive feature of hyperbolic equations is the finite propagation velocity of perturbations in the region of integration (wave processes) and the existence of characteristic manifolds: characteristic lines and surfaces (bounding the domains of dependence and influence of solutions). Another characteristic feature of equations and systems of hyperbolic equations is the appearance of discontinuous solutions in the nonlinear case even in the case of smooth (including analytic) boundary conditions: the so-called gradient catastrophe. In this paper, on the basis of the characteristic criterion for monotonicity, a universal algorithm is proposed for constructing high-order schemes monotone for arbitrary form of the sought-for solution, based on their analysis in the space of indefinite coefficients. The constructed high-order difference schemes are tested on the basis of the characteristic monotonicity criterion for nonlinear one-dimensional systems of hyperbolic equations.

Key words: hyperbolic equations, difference schemes, monotonicity criteria for difference schemes, high-order difference schemes.

Funding agency	Grant number
Russian Science Foundation	14-11-00877

Received: 26.03.2018

English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 8, Pages 1226–1246
DOI: https://doi.org/10.1134/S0965542518080110

Bibliographic databases:

Document Type: Article

UDC: 519.635

Language: Russian

Citation: Ya. A. Kholodov, A. S. Kholodov, I. V. Tsybulin, “Construction of monotone difference schemes for systems of hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 30–49; Comput. Math. Math. Phys., 58:8 (2018), 1226–1246

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/zvmmf10760

https://www.mathnet.ru/eng/zvmmf/v58/i8/p30

This publication is cited in the following 10 articles:

A. Yu. Trynin, “Ob odnom metode resheniya smeshannoi kraevoi zadachi dlya uravneniya parabolicheskogo tipa s pomoschyu operatorov $\mathbb{AT}_{\lambda,j}$ ”, Izv. vuzov. Matem., 2024, no. 2, 59–80
A. Yu. Trynin, “On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $\mathbb{A}{{\mathbb{T}}_{{\lambda ,j}}}$ ”, Russ Math., 68:2 (2024), 52
Victor V. Kuzenov, Sergei V. Ryzhkov, Aleksey Yu Varaksin, “Development of a method for solving elliptic differential equations based on a nonlinear compact-polynomial scheme”, Journal of Computational and Applied Mathematics, 451 (2024), 116098
A. Yu. Trynin, “A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$ ”, Izv. Math., 87:6 (2023), 1227–1254
N. I Khokhlov, I. B Petrov, “Setochno-kharakteristicheskiy metod povyshennogo poryadka dlya sistem giperbolicheskikh uravneniy s kusochno-postoyannymi koeffitsientami”, Differentsialnye uravneniya, 59:7 (2023), 983
A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284
N. I. Khokhlov, I. B. Petrov, “High-Order Grid-Characteristic Method for Systems of Hyperbolic Equations with Piecewise Constant Coefficients”, Diff Equat, 59:7 (2023), 985
V. Leviant, N. Marmalevsky, I. Kvasov, P. Stognii, I. Petrov, “Numerical modeling of seismic responses from fractured reservoirs in 4D monitoring - Part 1: Seismic responses from fractured reservoirs in carbonate and shale formations”, Geophysics, 86:6 (2021), M211–M232
Vladimir Leviant, Naum Marmalevsky, Igor Kvasov, Polina Stognii, Igor Petrov, “Numerical modeling of seismic responses from fractured reservoirs in 4D monitoring — Part 1: Seismic responses from fractured reservoirs in carbonate and shale formations”, GEOPHYSICS, 86:6 (2021), M211
Ya. A. Kholodov, “Razrabotka setevykh vychislitelnykh modelei dlya issledovaniya nelineinykh volnovykh protsessov na grafakh”, Kompyuternye issledovaniya i modelirovanie, 11:5 (2019), 777–814

Citing articles in Google Scholar: Russian citations, English citations
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