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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 12, Pages 1997–2007
DOI: https://doi.org/10.7868/S004446691312017X (Mi zvmmf9957) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Cubature formulas for a two-variable function with boundary-layer components

A. I. Zadorin

Omsk Branch of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644043, Russia
Full-text PDF (217 kB) Citations (2)
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DOI: https://doi.org/10.7868/S004446691312017X
Abstract: Cubature formulas for evaluating the double integral of a two-variable function with boundary-layer components are constructed and studied. Because of the boundary-layer components, the cubature formulas based on Newton–Cotes formulas become considerably less accurate. Analogues of the trapezoidal and Simpson rules that are exact for the boundary-layer components are constructed. Error estimates for the constructed formulas are derived that are uniform in the gradients of the integrand in the boundary layers.
Key words: two-variable function, boundary layer, double integral, nonpolynomial interpolation, cubature rule, error estimate.
Received: 11.04.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 12, Pages 1808–1818
DOI: https://doi.org/10.1134/S0965542513120130
Bibliographic databases:
Document Type: Article
UDC: 519.644.7
Language: Russian
Citation: A. I. Zadorin, “Cubature formulas for a two-variable function with boundary-layer components”, Zh. Vychisl. Mat. Mat. Fiz., 53:12 (2013), 1997–2007; Comput. Math. Math. Phys., 53:12 (2013), 1808–1818
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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