Geodesic
Quadrature formulas for functions with a boundary-layer component
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1952-1962 Cet article a éte moissonné depuis la source Math-Net.Ru

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Quadrature formulas for one-variable functions with a boundary-layer component are constructed and studied. It is assumed that the integrand can be represented as the sum of a regular and a boundary-layer component, the latter having high gradients that reduce the accuracy of classical quadrature formulas, such as the trapezoidal and Simpson rules. The formulas are modified so that their error is independent of the gradients of the boundary-layer component. Results of numerical experiments are presented. 
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A. I. Zadorin; N. A. Zadorin. Quadrature formulas for functions with a boundary-layer component. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1952-1962. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a1/

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