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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 490, Pages 35–41
DOI: https://doi.org/10.31857/S2686954320010221 (Mi danma29) 		 
This article is cited in 6 scientific papers (total in 6 papers)

MATHEMATICS

Stability of numerical methods for solving second-order hyperbolic equations with a small parameter

A. A. Zlotnikab, B. N. Chetverushkinb

a National Research University "Higher School of Economics", Moscow, Russian Federation
b Federal Research Center Keldysh Institute of Applied Mathmatics, Russian Academy of Sciences, Moscow, Russian Federation
Full-text PDF (289 kB) Citations (6)
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DOI: https://doi.org/10.31857/S2686954320010221
Abstract: We study a symmetric three-level (in time) method with a weight and a symmetric vector two-level method for solving the initial-boundary value problem for a second-order hyperbolic equation with a small parameter $\tau>0$ multiplying the highest time derivative, where the hyperbolic equation is a perturbation of the corresponding parabolic equation. It is proved that the solutions are uniformly stable in $\tau$ and time in two norms with respect to the initial data and the right-hand side of the equation. Additionally, the case where $\tau$ also multiplies the elliptic part of the equation is covered. The spacial discretization can be performed using the finite-difference or finite element method.
Keywords: second-order hyperbolic equations, small parameter, three- and two-level methods, uniform stability in small parameter and time.
Funding agency Grant number
Russian Science Foundation 19–11–00104
This work was supported by the Russian Science Foundation, project no. 19-11-00104.
Received: 06.09.2019
Revised: 06.09.2019
Accepted: 11.11.2019
English version:
Doklady Mathematics, 2020, Volume 101, Issue 1, Pages 30–35
DOI: https://doi.org/10.1134/S1064562420010226
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: A. A. Zlotnik, B. N. Chetverushkin, “Stability of numerical methods for solving second-order hyperbolic equations with a small parameter”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020), 35–41; Dokl. Math., 101:1 (2020), 30–35
Citation in format AMSBIB
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\by A.~A.~Zlotnik, B.~N.~Chetverushkin
\paper Stability of numerical methods for solving second-order hyperbolic equations with a small parameter
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\pages 35--41
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\zmath{https://zbmath.org/?q=an:07424545}
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\transl
\jour Dokl. Math.
\yr 2020
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\pages 30--35
\crossref{https://doi.org/10.1134/S1064562420010226}
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    • This publication is cited in the following 6 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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