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Sibirskii Zhurnal Industrial'noi Matematiki, 2018, Volume 21, Number 3, Pages 26–36
DOI: https://doi.org/10.17377/sibjim.2018.21.303 (Mi sjim1008) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Numerical solution of the retrospective inverse problem of heat conduction with the help of the Poisson integral

V. I. Vasil'ev, A. M. Kardashevskii

Ammosov North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000 Russia
Full-text PDF (737 kB) Citations (3) English version article
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DOI: https://doi.org/10.17377/sibjim.2018.21.303
Abstract: We consider the retrospective inverse problem that consists in determining the initial solution of the one-dimensional heat conduction equation with a given condition at the final instant of time. The solution of the problem is given in the form of the Poisson integral and is numerically realized by means of a quadrature formula leading to a system of linear algebraic equations with dense matrix. The results of numerical experiments are presented and show the efficiency of the numerical method including the case of the final condition with random errors.
Keywords: heat conduction equation, retrospective inverse problem of heat conduction, Poisson integral, integral equation, numerical method, system of linear equations, random errors.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00732
The authors were supported by the Russian Foundation for Basic Research (project no. 17-01-00732).
Received: 05.02.2018
Revised: 02.04.2018
English version:
Journal of Applied and Industrial Mathematics, 2018, Volume 12, Issue 3, Pages 577–586
DOI: https://doi.org/10.1134/S1990478918030158
Bibliographic databases:
Document Type: Article
UDC: 517.63
Language: Russian
Citation: V. I. Vasil'ev, A. M. Kardashevskii, “Numerical solution of the retrospective inverse problem of heat conduction with the help of the Poisson integral”, Sib. Zh. Ind. Mat., 21:3 (2018), 26–36; J. Appl. Industr. Math., 12:3 (2018), 577–586
Citation in format AMSBIB
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\by V.~I.~Vasil'ev, A.~M.~Kardashevskii
\paper Numerical solution of the retrospective inverse problem of heat conduction with the help of the Poisson integral
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 3
\pages 26--36
\mathnet{http://mi.mathnet.ru/sjim1008}
\crossref{https://doi.org/10.17377/sibjim.2018.21.303}
\elib{https://elibrary.ru/item.asp?id=36460639}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 3
\pages 577--586
\crossref{https://doi.org/10.1134/S1990478918030158}
\elib{https://elibrary.ru/item.asp?id=35731217}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052113149}
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    • This publication is cited in the following 3 articles:
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