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


Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 6, Pages 1020–1027
DOI: https://doi.org/10.7868/S0044466915030199
(Mi zvmmf10223)
 

This article is cited in 31 scientific papers (total in 31 papers)

Computational identification of the right-hand side of a parabolic equation

P. N. Vabishchevicha, V. l. Vasil'evb, M. V. Vasil'evab

a Nuclear Safety Institute, Russian Academy of Sciences, ul. Bol’shaya Tul’skaya 52, Moscow, 115191, Russia
b Ammosov North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000, Russia
References:
Abstract: Among inverse problems for partial differential equations, a task of interest is to study coefficient inverse problems related to identifying the right-hand side of an equation with the use of additional information. In the case of nonstationary problems, finding the dependence of the right-hand side on time and the dependence of the right-hand side on spatial variables can be treated as independent tasks. These inverse problems are linear, which considerably simplifies their study. The time dependence of the right-hand side of a multidimensional parabolic equation is determined using an additional solution value at a point of the computational domain. The inverse problem for a model equation in a rectangle is solved numerically using standard spatial difference approximations. The numerical algorithm relies on a special decomposition of the solution whereby the transition to a new time level is implemented by solving two standard grid elliptic problems. Numerical results are presented.
Key words: inverse problems, identification of coefficients, parabolic equation, difference schemes.
Received: 11.08.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 6, Pages 1015–1021
DOI: https://doi.org/10.1134/S0965542515030185
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: P. N. Vabishchevich, V. l. Vasil'ev, M. V. Vasil'eva, “Computational identification of the right-hand side of a parabolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:6 (2015), 1020–1027; Comput. Math. Math. Phys., 55:6 (2015), 1015–1021
Citation in format AMSBIB
\Bibitem{VabVasVas15}
\by P.~N.~Vabishchevich, V.~l.~Vasil'ev, M.~V.~Vasil'eva
\paper Computational identification of the right-hand side of a parabolic equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2015
\vol 55
\issue 6
\pages 1020--1027
\mathnet{http://mi.mathnet.ru/zvmmf10223}
\crossref{https://doi.org/10.7868/S0044466915030199}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3358010}
\elib{https://elibrary.ru/item.asp?id=23450661}
\transl
\jour Comput. Math. Math. Phys.
\yr 2015
\vol 55
\issue 6
\pages 1015--1021
\crossref{https://doi.org/10.1134/S0965542515030185}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000356505400009}
\elib{https://elibrary.ru/item.asp?id=23985568}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84935012140}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf10223
  • https://www.mathnet.ru/eng/zvmmf/v55/i6/p1020
  • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:440
    Full-text PDF :114
    References:61
    First page:27
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024