Geodesic
Quadrature formulas for functions with a boundary-layer component
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1952-1962

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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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     author = {A. I. Zadorin and N. A. Zadorin},
     title = {Quadrature formulas for functions with a~boundary-layer component},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1952--1962},
     publisher = {mathdoc},
     volume = {51},
     number = {11},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a1/}
}
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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/