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Mat. Zametki, 1996, Volume 60, Issue 5, Pages 751–759 (Mi mz1886)  

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

A three-time-level explicit difference scheme of the second order of accuracy for parabolic equations

A. S. Shvedov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: The difference schemes of Richardson [1] and of Crank–Nicolson [2] are schemes providing second-order approximation. Richardson's three-time-level difference scheme is explicit but unstable and the Crank–Nicolson two-time-level difference scheme is stable but implicit. Explicit numerical methods are preferable for parallel computations. In this paper, an explicit three-time-level difference scheme of the second order of accuracy is constructed for parabolic equations by combining Richardson's scheme with that of Crank–Nicolson. Restrictions on the time step required for the stability of the proposed difference scheme are similar to those that are necessary for the stability of the two-time-level explicit difference scheme, but the former are slightly less onerous.

DOI: https://doi.org/10.4213/mzm1886

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English version:
Mathematical Notes, 1996, 60:5, 562–568

Bibliographic databases:

UDC: 517
Received: 28.12.1995

Citation: A. S. Shvedov, “A three-time-level explicit difference scheme of the second order of accuracy for parabolic equations”, Mat. Zametki, 60:5 (1996), 751–759; Math. Notes, 60:5 (1996), 562–568

Citation in format AMSBIB
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\by A.~S.~Shvedov
\paper A three-time-level explicit difference scheme of the second order of accuracy for parabolic equations
\jour Mat. Zametki
\yr 1996
\vol 60
\issue 5
\pages 751--759
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\crossref{https://doi.org/10.4213/mzm1886}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619913}
\zmath{https://zbmath.org/?q=an:0897.65055}
\transl
\jour Math. Notes
\yr 1996
\vol 60
\issue 5
\pages 562--568
\crossref{https://doi.org/10.1007/BF02309170}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996WZ03000009}


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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. Shvedov, AS, “Explicit iterative difference schemes for parabolic equations”, Russian Journal of Numerical Analysis and Mathematical Modelling, 13:2 (1998), 133  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математические заметки Mathematical Notes
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