Geodesic
Modification of the Euler quadrature formula for functions with a boundary-layer component
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1547-1556 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. I. Zadorin. Modification of the Euler quadrature formula for functions with a boundary-layer component. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1547-1556. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a0/

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