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Mat. Zametki, 1972, Volume 12, Issue 2, Pages 177–186 (Mi mz9866)  

This article is cited in 1 scientific paper (total in 1 paper)

The approximate solution of singular integral equations

I. V. Boikov

Kazan State University

Abstract: A computational scheme of collocation type is proposed for a singular linear integral equation with a power singularity in the regular integral and the justification is given. The results obtained are used to justify the approximate solution of the singular integral equation
$$ K(x)\equiv a(t)x(t)+\frac{b(t)}{\pi i}\int_{|\tau|=1}\frac{x(\tau)d\tau}{\tau-t}+ \frac1{2\pi i}\int_{|\tau|=1}\frac{h(t,\tau)x(\tau)}{|\tau-t|^\delta}d\tau=f(t) $$
by a modification of the method of minimal residuals.

Full text: PDF file (891 kB)

English version:
Mathematical Notes, 1972, 12:2, 541–546

Bibliographic databases:

UDC: 513.88
Received: 13.10.1970

Citation: I. V. Boikov, “The approximate solution of singular integral equations”, Mat. Zametki, 12:2 (1972), 177–186; Math. Notes, 12:2 (1972), 541–546

Citation in format AMSBIB
\Bibitem{Boy72}
\by I.~V.~Boikov
\paper The approximate solution of singular integral equations
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 2
\pages 177--186
\mathnet{http://mi.mathnet.ru/mz9866}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=324929}
\zmath{https://zbmath.org/?q=an:0247.65071}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 2
\pages 541--546
\crossref{https://doi.org/10.1007/BF01095015}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Boikov I.V., Zakharova Yu.F., “Priblizhennye metody resheniya singulyarnykh i gipersingulyarnykh integrodifferentsialnykh uravnenii”, Izvestiya vysshikh uchebnykh zavedenii. povolzhskii region. fiziko-matematicheskie nauki, 2012, no. 3, 99–113  elib
  • Математические заметки Mathematical Notes
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