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 Trudy Inst. Mat. i Mekh. UrO RAN, 2017, Volume 23, Number 2, Pages 210–219 (Mi timm1423)

On the approximate solution of an inverse boundary value problem by the method of finite-dimensional approximation of the regularized solution

A. I. Sidikova

South Ural State University, Chelyabinsk

Abstract: We solve the inverse boundary value problem for the heat equation. The problem is reduced to an integral equation of the first kind, which in turn is reduced to a finite-dimensional equation by means of discretization in two variables. The latter equation is solved by means of A.N.Tikhonov's regularization method with the regularization parameter chosen according to the residual principle with discretization error taken into account. It is shown that the problem does not satisfy V.K. Ivanov's condition, which would allow to employ the modulus of continuity of the inverse operator. That is why, to estimate the error of the approximate solution, we propose a numerical approach using the discretization of the problem. The obtained estimate is compared with the classical estimate in terms of the modulus of continuity. The approach proposed in this paper makes it possible to considerably extend the class of problems to which it is applicable.

Keywords: ill-posed problem, integral equation, estimation of error, regularizing algorithm, finite-dimensional approximation.

 Funding Agency Grant Number Government of the Russian Federation 02.A03.21.0011

DOI: https://doi.org/10.21538/0134-4889-2017-23-2-210-219

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Bibliographic databases:

UDC: 517.948
MSC: 45B05, 45Q05

Citation: A. I. Sidikova, “On the approximate solution of an inverse boundary value problem by the method of finite-dimensional approximation of the regularized solution”, Trudy Inst. Mat. i Mekh. UrO RAN, 23, no. 2, 2017, 210–219

Citation in format AMSBIB
\Bibitem{Sid17} \by A.~I.~Sidikova \paper On the approximate solution of an inverse boundary value problem by the method of finite-dimensional approximation of the regularized solution \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2017 \vol 23 \issue 2 \pages 210--219 \mathnet{http://mi.mathnet.ru/timm1423} \crossref{https://doi.org/10.21538/0134-4889-2017-23-2-210-219} \elib{https://elibrary.ru/item.asp?id=29295263}