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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2014, Volume 11, Pages 258–267 (Mi semr486)  
This article is cited in 1 scientific paper (total in 1 paper)

Computational mathematics

Simpson rule and its modifications for a function with a boundary layer component

A. I. Zadorin, N. A. Zadorin

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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Abstract: Quadrature formulas for a function with a boundary layer component are investigated. An application of Simpson rule on an uniform mesh for the integration of such function leads to significant errors. Two approaches to increase the accuracy are investigated: the fitting of Simpson rule to a boundary layer component and using Simpson rule on Shishkin mesh. Results of numerical experiments are discussed.
Keywords: definite integral, singular perturbation, boundary layer component, Simpson rule, modification, Shishkin mesh, error estimation.
Received February 4, 2014, published April 1, 2014
Document Type: Article
UDC: 519.644
MSC: 65D32
Language: Russian
Citation: A. I. Zadorin, N. A. Zadorin, “Simpson rule and its modifications for a function with a boundary layer component”, Sib. Èlektron. Mat. Izv., 11 (2014), 258–267
Citation in format AMSBIB
\Bibitem{ZadZad14}
\by A.~I.~Zadorin, N.~A.~Zadorin
\paper Simpson rule and its modifications for a function with a boundary layer component
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 258--267
\mathnet{http://mi.mathnet.ru/semr486}
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