
Vestn. YuUrGU. Ser. Vych. Matem. Inform., 2016, Volume 5, Issue 1, Pages 35–46
(Mi vyurv100)




Computational Mathematics
On solution of solid state physics inverse problem by means of A. N. Tikhonov's regularization method and estimation of the error of this method
V. P. Tanana^{}, A. I. Sidikova^{} ^{} South Ural State University, Chelyabinsk, Russian Federation
Abstract:
The paper considers onedimensional Fredholm integral equation of the first kind with a closed core. It is known that the equation has a unique solution in the space $W^1_{2}[a, b]$. We use Tikhonov's regularization method of the firstorder to solve the equation. The method allows us to reduce the equation to a variational problem. Solving the variational problem we get integrodifferential equation of second order. We apply the finitedifference approximation method to reduce the original problem to a system of algebraic equations. regularization parameter.
We obtain an error estimate for the proposed algorithm taking into account the error of finitedifference approximation and state the relation between the approximation with the error and the regularization parameter and the error of the initial data.
This algorithm is used to solve the problem of determining the phonon spectrum of the crystal given its heat capacity.
Keywords:
regularization, the method of residuals, the modulus of continuity, error estimation, illposed problem.
DOI:
https://doi.org/10.14529/cmse160104
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UDC:
517.968.21 Received: 10.09.2015
Citation:
V. P. Tanana, A. I. Sidikova, “On solution of solid state physics inverse problem by means of A. N. Tikhonov's regularization method and estimation of the error of this method”, Vestn. YuUrGU. Ser. Vych. Matem. Inform., 5:1 (2016), 35–46
Citation in format AMSBIB
\Bibitem{TanSid16}
\by V.~P.~Tanana, A.~I.~Sidikova
\paper On solution of solid state physics inverse problem by means of A.~N. Tikhonov's regularization method and estimation of the error of this method
\jour Vestn. YuUrGU. Ser. Vych. Matem. Inform.
\yr 2016
\vol 5
\issue 1
\pages 3546
\mathnet{http://mi.mathnet.ru/vyurv100}
\crossref{https://doi.org/10.14529/cmse160104}
\elib{http://elibrary.ru/item.asp?id=25629791}
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