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 Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 5, Pages 848–857 (Mi zvmmf470)

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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:5, 810–819

Bibliographic databases:

UDC: 519.633.9

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
\Bibitem{GluKar06} \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://www.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}