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Modification of the Euler quadrature formula for functions with a boundary-layer component
A. I. Zadorin Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644043, Russia
Abstract:
The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate quadrature formula is constructed by modifying the Hermite interpolation formula so that the resulting one is exact for the boundary-layer component. An analogue of the Euler formula that is exact for the boundary-layer component is constructed. It is proved that the resulting composite quadrature formula is third-order accurate in space uniformly with respect to the boundary-layer component and its derivatives.
Key words:
quadrature formula for definite integrals, function with a boundary-layer component, modified Euler quadrature formula, Hermite polynomial, modification, error estimate for quadrature formulas.
Received: 28.11.2013
Citation:
A. I. Zadorin, “Modification of the Euler quadrature formula for functions with a boundary-layer component”, Zh. Vychisl. Mat. Mat. Fiz., 54:10 (2014), 1547–1556; Comput. Math. Math. Phys., 54:10 (2014), 1489–1498
Linking options:
https://www.mathnet.ru/eng/zvmmf10092 https://www.mathnet.ru/eng/zvmmf/v54/i10/p1547
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Abstract page: | 377 | Full-text PDF : | 138 | References: | 49 | First page: | 6 |
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