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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 8, Pages 30–49 (Mi zvmmf10760)  

This article is cited in 1 scientific paper (total in 1 paper)

Construction of monotone difference schemes for systems of hyperbolic equations

Ya. A. Kholodovab, A. S. Kholodovca, I. V. Tsybulinc

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

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


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

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:8, 1226–1246

Bibliographic databases:

UDC: 519.635
Received: 26.03.2018

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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\paper Construction of monotone difference schemes for systems of hyperbolic equations
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\vol 58
\issue 8
\pages 30--49
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\transl
\jour Comput. Math. Math. Phys.
\yr 2018
\vol 58
\issue 8
\pages 1226--1246
\crossref{https://doi.org/10.1134/S0965542518080110}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ya. A. Kholodov, “Razrabotka setevykh vychislitelnykh modelei dlya issledovaniya nelineinykh volnovykh protsessov na grafakh”, Kompyuternye issledovaniya i modelirovanie, 11:5 (2019), 777–814  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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