S. K. Godunov, V. T. Zhukov, O. B. Feodoritova, “A method for calculating invariant subspaces of symmetric hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 1019–1031; Comput. Math. Math. Phys., 46:6 (2006), 971

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 6, Pages 1019–1031 (Mi zvmmf456)

This article is cited in 8 scientific papers (total in 9 papers)

A method for calculating invariant subspaces of symmetric hyperbolic equations

S. K. Godunov^a, V. T. Zhukov^b, O. B. Feodoritova^b

^a Sobolev Institute of Mathematics, Siberian Division, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia
^b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

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Abstract: An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.

Key words: symmetric hyperbolic systems, method for calculating invariant subspaces, calculation of eigenvalues and eigenfunctions.

Received: 12.12.2005

English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 6, Pages 971–982
DOI: https://doi.org/10.1134/S0965542506060066

Bibliographic databases:

Document Type: Article

UDC: 519.633

Language: Russian

Citation: S. K. Godunov, V. T. Zhukov, O. B. Feodoritova, “A method for calculating invariant subspaces of symmetric hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 1019–1031; Comput. Math. Math. Phys., 46:6 (2006), 971–982

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/zvmmf456

https://www.mathnet.ru/eng/zvmmf/v46/i6/p1019

This publication is cited in the following 9 articles:

D. L. Tkachev, A. V. Yegitov, E. A. Biberdorf, “Linear instability of a resting state of the magnetohydrodynamic flows of polymeric fluid in a cylindrical channel (generalized Vinogradov–Pokrovski model)”, Physics of Fluids, 36:9 (2024)
V. V. Skazka, “Kososimmetricheskie raznostnye analogi chetvertogo poryadka approksimatsii pervoi proizvodnoi”, Sib. zhurn. industr. matem., 25:4 (2022), 179–192
V. V. Skazka, “Skew-Symmetric Difference Analogs of the Fourth-Order Approximation to the First Derivative”, J. Appl. Ind. Math., 16:4 (2022), 789
Romanovskii R.K., Nazaruk E.M., “Spektralnyi kriterii eksponentsialnoi dikhotomii dlya lineinoi avtonomnoi sistemy funktsionalno-differentsialnykh uravnenii”, Doklady Akademii nauk vysshei shkoly Rossiiskoi Federatsii, 2012, no. 1, 19–27
Nazaruk E.M., Romanovskaya A.M., “Ob eksponentsialnoi dikhotomii reshenii zadachi koshi dlya sistemy differentsialno-raznostnykh uravnenii s postoyannymi koeffitsientami”, Vestnik omskogo universiteta, 2011, no. 4, 45–49 On the exponential dichotomy of cauchy problem solutions for systems of difference-differential equations with constant coefficients
K. V. Brushlinskiǐ, V. G. Zhukov, M. K. Kerimov, “Academician SergeĭKonstantinovich Godunov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 50:1 (2010), 1–6
S.K. Godunov, O.B. Feodoritova, V.T. Zhukov, Computational Fluid Dynamics 2006, 2009, 143
S. K. Godunov, Hyperbolic Problems: Theory, Numerics, Applications, 2008, 19
D. P. Babii, S. K. Godunov, V. T. Zhukov, O. B. Feodoritova, “On the difference approximations of overdetermined hyperbolic equations of classical mathematical physics”, Comput. Math. Math. Phys., 47:3 (2007), 427–441

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

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