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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, Number 9, Pages 27–39 (Mi ivm1709)  
Direct methods for solving singular integral equations with nonnegative indices

V. I. Kas'yanov

Almet'evsk State Petroleum Institute, Almet'evsk, Russia
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Abstract: In this paper we consider a complete singular integral equation with the Cauchy kernel on the real axis and a bisingular integral equation on a plane with a degenerate characteristic part. We theoretically substantiate the polynomial methods of moments and collocation in the case of nonnegative indices. We also prove the convergence of the method of mechanical quadratures for the corresponding one-dimensional equation.
Keywords: singular integral on the real axis, linear one-dimensional and two-dimensional equations, direct method, convergence of a method.
Received: 02.06.2006
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2008, Volume 52, Issue 8, Pages 23–34
DOI: https://doi.org/10.3103/S1066369X08090041
Bibliographic databases:
UDC: 517.544
Language: Russian
Citation: V. I. Kas'yanov, “Direct methods for solving singular integral equations with nonnegative indices”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 9, 27–39; Russian Math. (Iz. VUZ), 52:8 (2008), 23–34
Citation in format AMSBIB
\Bibitem{Kas08}
\by V.~I.~Kas'yanov
\paper Direct methods for solving singular integral equations with nonnegative indices
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2008
\issue 9
\pages 27--39
\mathnet{http://mi.mathnet.ru/ivm1709}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2468304}
\zmath{https://zbmath.org/?q=an:1176.65158}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2008
\vol 52
\issue 8
\pages 23--34
\crossref{https://doi.org/10.3103/S1066369X08090041}
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