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 Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 93–102 (Mi smj9)

Study of convergence of the projection-difference method for hyperbolic equations

S. E. Zhelezovsky

Saratov State Socio-Economic University

Abstract: We consider the Cauchy problem for an abstract quasilinear hyperbolic equation with variable operator coefficients and a nonsmooth but Bochner integrable free term in a Hilbert space. Under study is the scheme for approximate solution of this problem which is a combination of the Galerkin scheme in space variables and the three-layer difference scheme with time weights. We establish an a priori energy error estimate without any special conditions on the projection subspaces. We give a concrete form of this estimate in the case when discretization in the space variables is carried out by the finite element method (for a partial differential equation) and by the Galerkin method in Mikhlin form.

Keywords: abstract hyperbolic equation, projection-difference method, Galerkin method, three-layer difference scheme, error estimate.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 76–83

Bibliographic databases:

UDC: 517.988.8
Revised: 15.03.2006

Citation: S. E. Zhelezovsky, “Study of convergence of the projection-difference method for hyperbolic equations”, Sibirsk. Mat. Zh., 48:1 (2007), 93–102; Siberian Math. J., 48:1 (2007), 76–83

Citation in format AMSBIB
\Bibitem{Zhe07} \by S.~E.~Zhelezovsky \paper Study of convergence of the projection-difference method for hyperbolic equations \jour Sibirsk. Mat. Zh. \yr 2007 \vol 48 \issue 1 \pages 93--102 \mathnet{http://mi.mathnet.ru/smj9} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2304881} \zmath{https://zbmath.org/?q=an:1164.65462} \transl \jour Siberian Math. J. \yr 2007 \vol 48 \issue 1 \pages 76--83 \crossref{https://doi.org/10.1007/s11202-007-0009-1} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000244424100009} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846613163} 

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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. Gavrilov V.S., “Existence and Uniqueness of Solutions of Hyperbolic Equations in Divergence Form With Various Boundary Conditions on Various Parts of the Boundary”, Differ. Equ., 52:8 (2016), 1011–1022
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