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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 101–110
DOI: https://doi.org/10.17377/semi.2016.13.008 (Mi semr686) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Computational mathematics

Gauss quadrature on a piecewise uniform mesh for functions with large gradients in a boundary layer

A. I. Zadorin

Sobolev Institute of Mathematics, Omsk branch, ul. Pevtsova, 13, 644043, Omsk, Russia
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DOI: https://doi.org/10.17377/semi.2016.13.008
Abstract: Gauss quadrature for a function with large gradients in the exponential boundary layer is investigated. In the case of such function the application of Gauss formula on the uniform grid leads to significant errors. The accuracy of Gauss quadrature on Shishkin mesh is investigated. The error of the quadrature formula is estimated. This estimate is uniform with respect to the small parameter. Results of numerical experiments are discussed.
Keywords: definite integral, boundary layer, large gradients, Gauss quadrature, Shishkin mesh, error estimation.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-06584_а
16-01-00727_а
Received January 26, 2016, published February 26, 2016
Document Type: Article
UDC: 519.644
MSC: 65D32
Language: Russian
Citation: A. I. Zadorin, “Gauss quadrature on a piecewise uniform mesh for functions with large gradients in a boundary layer”, Sib. Èlektron. Mat. Izv., 13 (2016), 101–110
Citation in format AMSBIB
\Bibitem{Zad16}
\by A.~I.~Zadorin
\paper Gauss quadrature on a piecewise uniform mesh for functions with large gradients in a boundary layer
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 101--110
\mathnet{http://mi.mathnet.ru/semr686}
\crossref{https://doi.org/10.17377/semi.2016.13.008}
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