Geodesic
An analogue of Newton–Cotes formula with four nodes for a function with a boundary-layer component
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 313-323 Cet article a éte moissonné depuis la source Math-Net.Ru

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The construction of the Newton–Cotes formulas is based on approximating an integrand by the Lagrange polynomial. The error of such quadrature formulas can be serious for a function with a boundary-layer component. In this paper, an analogue to the Newton–Cotes rule with four nodes is constructed. The construction is based on using non-polynomial interpolation that is accurate for a boundary layer component. Estimates of the accuracy of the quadrature rule, uniform on gradients of the boundary layer component, are obtained. Numerical experiments have been performed. 
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     title = {An analogue of {Newton{\textendash}Cotes} formula with four nodes for a~function with a~boundary-layer component},
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A. I. Zadorin; N. A. Zadorin. An analogue of Newton–Cotes formula with four nodes for a function with a boundary-layer component. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 4, pp. 313-323. http://geodesic.mathdoc.fr/item/SJVM_2013_16_4_a1/

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