RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. YuUrGU. Ser. Vych. Matem. Inform.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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 one-dimensional 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 first-order to solve the equation. The method allows us to reduce the equation to a variational problem. Solving the variational problem we get integro-differential equation of second order. We apply the finite-difference 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 finite-difference 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, ill-posed problem.

DOI: https://doi.org/10.14529/cmse160104

Full text: PDF file (452 kB)
References: PDF file   HTML file

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 35--46
\mathnet{http://mi.mathnet.ru/vyurv100}
\crossref{https://doi.org/10.14529/cmse160104}
\elib{http://elibrary.ru/item.asp?id=25629791}


Linking options:
  • http://mi.mathnet.ru/eng/vyurv100
  • http://mi.mathnet.ru/eng/vyurv/v5/i1/p35

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Vychislitelnaya Matematika i Informatika"
    Number of views:
    This page:232
    Full text:82
    References:25

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020