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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 3, Pages 368–376
DOI: https://doi.org/10.7868/S0044466916030194 (Mi zvmmf10360) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component

A. I. Zadorin, N. A. Zadorin

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644043, Russia
Full-text PDF (111 kB) Citations (6)
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DOI: https://doi.org/10.7868/S0044466916030194
Abstract: The numerical integration of functions with a boundary-layer component whose derivatives are not uniformly bounded is investigated. The Newton-Cotes formulas as applied to such functions can lead to significant errors. An analogue of Newton-Cotes formulas that is exact for the boundary-layer component is constructed. For the resulting formula, an error estimate that is uniform with respect to the boundary-layer component and its derivatives is obtained. Numerical results that agree with the error estimates are presented.
Key words: one-variable functions with a boundary-layer component, definite integral, modification of Newton–Cotes formulas, error estimate.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00618_а
15-01-06584_а
Received: 08.12.2014
Revised: 22.04.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 3, Pages 358–366
DOI: https://doi.org/10.1134/S0965542516030179
Bibliographic databases:
Document Type: Article
UDC: 519.644
Language: Russian
Citation: A. I. Zadorin, N. A. Zadorin, “Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component”, Zh. Vychisl. Mat. Mat. Fiz., 56:3 (2016), 368–376; Comput. Math. Math. Phys., 56:3 (2016), 358–366
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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