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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 5, Pages 848–857 (Mi zvmmf470)  
This article is cited in 4 scientific papers (total in 4 papers)

Numerical solution of the linear inverse problem for the Euler–Darboux equation

A. V. Glushaka, T. T. Karakeevb

a Belgorod State University, ul. Pobedy 85, Belgorod, 308015, Russia
b Kyrgyz National University, ul. Abdumomunova 328, Bishkek, 720033, Kyrgyzstan
Full-text PDF (811 kB) Citations (4)
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Abstract: An inverse problem of the reconstruction of the right-hand side of the Euler–Darboux equation is studied. This problem is equivalent to the Volterra integral equation of the third kind with the operator of multiplication by a smooth nonincreasing function. Numerical solution of this problem is constructed using an integral representation of the solution of the inverse problem, the regularization method, and the method of quadratures. The convergence and stability of the numerical method is proved.
Key words: inverse problem, Volterra equation of the third kind, regularization, numerical solution, stability.
Received: 06.04.2005
English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 5, Pages 810–819
DOI: https://doi.org/10.1134/S0965542506050071
Bibliographic databases:
Document Type: Article
UDC: 519.633.9
Language: Russian
Citation: A. V. Glushak, T. T. Karakeev, “Numerical solution of the linear inverse problem for the Euler–Darboux equation”, Zh. Vychisl. Mat. Mat. Fiz., 46:5 (2006), 848–857; Comput. Math. Math. Phys., 46:5 (2006), 810–819
Citation in format AMSBIB
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\by A.~V.~Glushak, T.~T.~Karakeev
\paper Numerical solution of the linear inverse problem for the Euler--Darboux equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 5
\pages 848--857
\mathnet{http://mi.mathnet.ru/zvmmf470}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2286280}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 5
\pages 810--819
\crossref{https://doi.org/10.1134/S0965542506050071}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746058209}
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  • https://www.mathnet.ru/eng/zvmmf/v46/i5/p848
    • This publication is cited in the following 4 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
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    Full-text PDF :139
    References:43
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