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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 10, Pages 1547–1556 (Mi zvmmf10092)  

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.

DOI: https://doi.org/10.7868/S0044466914100081

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:10, 1489–1498

Bibliographic databases:

UDC: 519.644.2
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

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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