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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 5, Pages 35–43 (Mi ivm7301)  

Approximate solution of one singular integro-differential equation

I. N. Meleshko, P. G. Lasy

Chair of Higher Mathematics № 2, Belarussian National Technical University, Minsk, Republic of Belarus
References:
Abstract: In this paper we construct and theoretically justify a computational scheme for solving the Cauchy problem for a singular integro-differential equation of the first-order, where the integral over a segment of the real axis is understood in the sense of the Cauchy principal value. In addition, we study and solve approximately the integral equation with a special logarithmic kernel. We obtain uniform estimates for errors of approximate formulas. Orders of errors of approximate solutions are proved to be proportional to the order of the approximation error for the derivative of the density of the singular integral in the integro-differential equation.
Keywords: integro-differential equation, approximate solution, quadrature formula, logarithmic kernel, Prandtl equation.
Received: 09.12.2009
Revised: 07.04.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 5, Pages 28–34
DOI: https://doi.org/10.3103/S1066369X11050057
Bibliographic databases:
Document Type: Article
UDC: 517.968+519.6
Language: Russian
Citation: I. N. Meleshko, P. G. Lasy, “Approximate solution of one singular integro-differential equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 5, 35–43; Russian Math. (Iz. VUZ), 55:5 (2011), 28–34
Citation in format AMSBIB
\Bibitem{MelLas11}
\by I.~N.~Meleshko, P.~G.~Lasy
\paper Approximate solution of one singular integro-differential equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 5
\pages 35--43
\mathnet{http://mi.mathnet.ru/ivm7301}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2920087}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 5
\pages 28--34
\crossref{https://doi.org/10.3103/S1066369X11050057}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051658432}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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