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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
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.
Received: 08.12.2014 Revised: 22.04.2015
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10360 https://www.mathnet.ru/eng/zvmmf/v56/i3/p368
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