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

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

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
Received: 15.06.2005
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
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\paper Study of convergence of the projection-difference method for hyperbolic equations
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\yr 2007
\vol 48
\issue 1
\pages 93--102
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\transl
\jour Siberian Math. J.
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\vol 48
\issue 1
\pages 76--83
\crossref{https://doi.org/10.1007/s11202-007-0009-1}
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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  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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