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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2016, Volume 19, Number 1, Pages 97–105
DOI: https://doi.org/10.15372/SJNM20160108 (Mi sjvm605) 		 
This article is cited in 12 scientific papers (total in 12 papers)

About an approximate solution to the Fredholm integral equation of the first kind by the residual method

V. P. Tanana, E. Y. Vishnyakov, A. I. Sidikova

South Ural State University, 76 Lenin pr., Chelyabinsk, 454080, Russia
Full-text PDF (424 kB) Citations (12)
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DOI: https://doi.org/10.15372/SJNM20160108
Abstract: The Tikhonov finite-dimensional approximation was applied to an integral equation of the first kind. This allowed us to use the variation regularization method of choosing the regularization parameter residuals from the principle of reducing the problem to a system of linear algebraic equations. The estimate of accuracy of the approximate solution with allowance for the error of the finite-dimensional problem approximation has been obtained. The use of this approach is illustrated on an example of solving an inverse boundary value problem for the heat conductivity equation.
Key words: regularization, method of residuals, module of continuity, evaluation of inaccuracy, ill-posed problem.
Received: 27.03.2015
Revised: 19.05.2015
English version:
Numerical Analysis and Applications, 2016, Volume 9, Issue 1, Pages 74–81
DOI: https://doi.org/10.1134/S1995423916010080
Bibliographic databases:
Document Type: Article
UDC: 517.948
Language: Russian
Citation: V. P. Tanana, E. Y. Vishnyakov, A. I. Sidikova, “About an approximate solution to the Fredholm integral equation of the first kind by the residual method”, Sib. Zh. Vychisl. Mat., 19:1 (2016), 97–105; Num. Anal. Appl., 9:1 (2016), 74–81
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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