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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2015, Volume 15, Issue 3, Pages 309–314
DOI: https://doi.org/10.18500/1816-9791-2015-15-3-309-314
(Mi isu597)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

The solution of the problem of determining the density of heat sources in a rod

A. A. Khromov, G. V. Khromova

Saratov State University, 83, Astrakhanskaya st., 410012, Saratov, Russia
Full-text PDF (147 kB) Citations (2)
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Abstract: We give a solution of a problem of determining the density of heat sources in the bav, which is set to a fixed temperature, if the temperature is given approximately. Mathematically it is the problem of finding uniform approximations to the right-hand side of the ordinary differential equation when uniform approximations to the solution and values of error are known. First using the so-called discontinuous Steklov operator we construct families of operators which give stable uniform approximations to a function and its first and second derivatives, and then with their help we propose the method of solving the formulated problem. For a certain class of solutions error estimations are given.
Key words: inverse problem, Steklov operator, regularization.
Bibliographic databases:
Document Type: Article
UDC: 519.642.8
Language: Russian
Citation: A. A. Khromov, G. V. Khromova, “The solution of the problem of determining the density of heat sources in a rod”, Izv. Saratov Univ. Math. Mech. Inform., 15:3 (2015), 309–314
Citation in format AMSBIB
\Bibitem{KhrKhr15}
\by A.~A.~Khromov, G.~V.~Khromova
\paper The solution of the problem of determining the density of heat sources in a rod
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 3
\pages 309--314
\mathnet{http://mi.mathnet.ru/isu597}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-3-309-314}
\elib{https://elibrary.ru/item.asp?id=24235224}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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