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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2015, Volume 18, Number 3, Pages 327–335
DOI: https://doi.org/10.15372/SJNM20150307
(Mi sjvm585)
 

This article is cited in 14 scientific papers (total in 14 papers)

A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind

S. V. Solodushaa, N. M. Yaparovab

a Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, 130 Lermontov str., Irkutsk, 664033, Russia
b South Ural State University, 76 Lenin pr., Chelyabinsk, 454080, Russia
References:
Abstract: We consider an inverse boundary value problem of heat conduction. To solve it, we propose a new approach based on the Laplace transform. This approach allows us to confine the original problem to solving the Volterra equations of the first kind. We have developed algorithms of the numerical solution to the resulting integral equations. The algorithms developed are based on the application of the product integration method and the quadrature of middle rectangles. A series of test calculations were performed to test the efficiency of the numerical methods.
Key words: Volterra integral equations, numerical solution, product integration method.
Received: 07.07.2014
Revised: 17.10.2014
English version:
Numerical Analysis and Applications, 2015, Volume 8, Issue 3, Pages 267–274
DOI: https://doi.org/10.1134/S1995423915030076
Bibliographic databases:
Document Type: Article
UDC: 519.642.5
Language: Russian
Citation: S. V. Solodusha, N. M. Yaparova, “A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind”, Sib. Zh. Vychisl. Mat., 18:3 (2015), 327–335; Num. Anal. Appl., 8:3 (2015), 267–274
Citation in format AMSBIB
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\by S.~V.~Solodusha, N.~M.~Yaparova
\paper A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind
\jour Sib. Zh. Vychisl. Mat.
\yr 2015
\vol 18
\issue 3
\pages 327--335
\mathnet{http://mi.mathnet.ru/sjvm585}
\crossref{https://doi.org/10.15372/SJNM20150307}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3492617}
\elib{https://elibrary.ru/item.asp?id=23907304}
\transl
\jour Num. Anal. Appl.
\yr 2015
\vol 8
\issue 3
\pages 267--274
\crossref{https://doi.org/10.1134/S1995423915030076}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84938576574}
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  • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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