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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 4, Pages 15–22 (Mi vmj593)  

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

Approximate solution of a singular integral equation using Chebyshev series

Z. V. Besaevaa, Sh. S. Khubezhtybc

a South-Ossetia State University, Tskhinval
b North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences

Abstract: A new method of approximate solution of singular integral equations with application of Chebyshev series is offered. Decomposition coefficients are determined by means of the solution of systems of simple algebraic equations. A justification of the constructed computational scheme is given and error estimate is deduced. The method is illustrated by test examples.

Key words: singular integral, Chebyshev series, approximation of integral, error estimation, orthogonal polynomial, coefficient of expansion.

Full text: PDF file (199 kB)
References: PDF file   HTML file
UDC: 517.392
Received: 30.03.2015

Citation: Z. V. Besaeva, Sh. S. Khubezhty, “Approximate solution of a singular integral equation using Chebyshev series”, Vladikavkaz. Mat. Zh., 18:4 (2016), 15–22

Citation in format AMSBIB
\Bibitem{BesKhu16}
\by Z.~V.~Besaeva, Sh.~S.~Khubezhty
\paper Approximate solution of a singular integral equation using Chebyshev series
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 4
\pages 15--22
\mathnet{http://mi.mathnet.ru/vmj593}


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    This publication is cited in the following articles:
    1. Sh. S. Khubezhty, “Priblizhennoe reshenie singulyarnykh integralnykh uravnenii s primeneniem ryadov Chebysheva na klasse funktsii, obraschayuschikhsya v nul na odnom kontse i v beskonechnost na drugom kontse intervala integrirovaniya”, Sib. zhurn. vychisl. matem., 24:3 (2021), 331–341  mathnet  crossref
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