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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.
DOI:
https://doi.org/10.31857/S004446690001999-9
References:
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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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\jour Comput. Math. Math. Phys.
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\pages 1226--1246
\crossref{https://doi.org/10.1134/S0965542518080110}
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http://mi.mathnet.ru/eng/zvmmf10760 http://mi.mathnet.ru/eng/zvmmf/v58/i8/p30
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Ya. A. Kholodov, “Razrabotka setevykh vychislitelnykh modelei dlya issledovaniya nelineinykh volnovykh protsessov na grafakh”, Kompyuternye issledovaniya i modelirovanie, 11:5 (2019), 777–814
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