Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component (Q2630031)

The objective of this article is to design a general quadrature formula for the boundary-layer component whose derivatives are not uniformly bounded. Such functions belongs to the class of function-solutions of singularly perturbed boundary value problems widely studied in the scientific school of Professor Shishkin, see the monograph by \textit{J. J. H. Miller} et al. [Fitted numerical methods for singular perturbation problems. Error estimates in the maximum norm for linear problems in one and two dimensions. Revised ed. Hackensack, NJ: World Scientific (2012; Zbl 1243.65002)]. An analogue of Newton-Cotes formulas that is exact for the boundary-layer component is constructed. Error estimates that are uniform with respect to the boundary-layer component and its derivatives are obtained. The efficiency of proposed quadrature is demonstrated on numerical examples with synthetic data.