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Mathematical notes of NEFU, 2017, Volume 24, Issue 3, Pages 38–51
DOI: https://doi.org/10.25587/SVFU.2018.3.10888
(Mi svfu189)
 

Mathematical modeling

Iterative method for the Dirichlet problem and its modifications

V. I. Vasilieva, A. M. Kardashevskya, V. V. Popovab

a M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 58 Belinsky Street, Yakutsk, 677000 Russia
b Institute of Oil and Gas Problems SB RAS, 1 Oktyabrskaya Street, Yakutsk 677000, Russia
References:
Abstract: A series of works of S. I. Kabanikhin's scientific school are devoted to study of the existence, uniqueness, and numerical methods for the inverse Dirichlet problem for the second-order hyperbolic equations. We consider a numerical solution to the non-classical Dirichlet problem and its modifications for the two-dimensional hyperbolic second-order equations. The method of iterative refinement of the missing initial condition is applied by means of an additional condition specified at the final time. Moreover, the direct problem is numerically realized at each iteration. The efficiency of the proposed computational algorithm is confirmed by calculations for two-dimensional model problems, including additional conditions with random errors.
Keywords: hyperbolic equation, inverse problem, Dirichlet problem, finite difference method, iterative method, conjugate gradients method, random error.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00732_а
The work was supported by a grant from the Russian Foundation for Basic Research (project code 17.01.000732).
Received: 04.08.2017
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: V. I. Vasiliev, A. M. Kardashevsky, V. V. Popov, “Iterative method for the Dirichlet problem and its modifications”, Mathematical notes of NEFU, 24:3 (2017), 38–51
Citation in format AMSBIB
\Bibitem{VasKarPop17}
\by V.~I.~Vasiliev, A.~M.~Kardashevsky, V.~V.~Popov
\paper Iterative method for the Dirichlet problem and its modifications
\jour Mathematical notes of NEFU
\yr 2017
\vol 24
\issue 3
\pages 38--51
\mathnet{http://mi.mathnet.ru/svfu189}
\crossref{https://doi.org/10.25587/SVFU.2018.3.10888}
\elib{https://elibrary.ru/item.asp?id=32651434}
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