Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 6, Pages 1002–1009 (Mi zvmmf9618)  

This article is cited in 4 scientific papers (total in 4 papers)

SM-stability of operator-difference schemes

P. N. Vabishchevich

Nuclear Safety Institute, RAS

Abstract: The spectral mimetic (SM) properties of operator-difference schemes for solving the Cauchy problem for first-order evolutionary equations concern the time evolution of individual harmonics of the solution. Keeping track of the spectral characteristics makes it possible to select more appropriate approximations with respect to time. Among two-level implicit schemes of improved accuracy based on Padй approximations, SM-stability holds for schemes based on polynomial approximations if the operator in an evolutionary equation is self-adjoint and for symmetric schemes if the operator is skew-symmetric. In this paper, additive schemes (also called splitting schemes) are constructed for evolutionary equations with general operators. These schemes are based on the extraction of the self-adjoint and skew-symmetric components of the corresponding operator.

Key words: Cauchy problem, first-order evolutionary equation, operator-difference schemes, stability

Full text: PDF file (189 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2012, 52:6, 887–894

Bibliographic databases:

UDC: 519.63
Received: 18.04.2011

Citation: P. N. Vabishchevich, “SM-stability of operator-difference schemes”, Zh. Vychisl. Mat. Mat. Fiz., 52:6 (2012), 1002–1009; Comput. Math. Math. Phys., 52:6 (2012), 887–894

Citation in format AMSBIB
\Bibitem{Vab12}
\by P.~N.~Vabishchevich
\paper SM-stability of operator-difference schemes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2012
\vol 52
\issue 6
\pages 1002--1009
\mathnet{http://mi.mathnet.ru/zvmmf9618}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3245175}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012CMMPh..52..887V}
\elib{https://elibrary.ru/item.asp?id=17745728}
\transl
\jour Comput. Math. Math. Phys.
\yr 2012
\vol 52
\issue 6
\pages 887--894
\crossref{https://doi.org/10.1134/S0965542512060140}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305735100006}
\elib{https://elibrary.ru/item.asp?id=20472832}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84863207101}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf9618
  • http://mi.mathnet.ru/eng/zvmmf/v52/i6/p1002

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. M. A. Sultanov, “Otsenki ustoichivosti reshenii trekhsloinoi raznostnoi skhemy s dvumya vesami dlya nekorrektnykh zadach Koshi”, Sib. elektron. matem. izv., 12 (2015), 28–44  mathnet  crossref
    2. P. N. Vabishchevich, “Factorized schemes of second-order accuracy for numerically solving unsteady problems”, Comput. Methods Appl. Math., 17:2 (2017), 323–335  crossref  mathscinet  zmath  isi  scopus
    3. M. A. Sultanov, M. I. Akylbaev, R. Ibragimov, “Conditional stability of a solution of a difference scheme for an ill-posed cauchy problem”, Electron. J. Differ. Equ., 2018, 33  mathscinet  zmath  isi
    4. A. V. Avvakumov, V. F. Strizhov, P. N. Vabishchevich, A. O. Vasilev, “State change modal method for numerical simulation of dynamic processes in a nuclear reactor”, Prog. Nucl. Energy, 106 (2018), 240–261  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:287
    Full text:71
    References:38
    First page:10

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021