Geodesic
The Lagrange interpolation and the Newton--Cotes formulas for functions with a~boundary layer component on piecewise-uniform meshes
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 289-303.

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The interpolation problem of a one-variable function, which can be considered as a solution of a boundary value problem for an equation with a small parameter $\varepsilon$ with a higher derivative is investigated. The application of the Lagrange interpolation for such a function on a uniform grid can result in serious errors. In the case of the Shishkin mesh, $\varepsilon$-uniform error estimates of the Lagrange interpolation are obtained. The Shishkin mesh is modified to increase the interpolation accuracy. The $\varepsilon$-uniform error estimates of the Newton–Cotes formulas on such meshes are obtained. Numerical experiments have been carried out. The results obtained confirm the theoretical estimates. 
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A. I. Zadorin. The Lagrange interpolation and the Newton--Cotes formulas for functions with a~boundary layer component on piecewise-uniform meshes. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 289-303. http://geodesic.mathdoc.fr/item/SJVM_2015_18_3_a3/

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