Geodesic
Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 368-376

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The numerical integration of functions with a boundary-layer component whose derivatives are not uniformly bounded is investigated. The Newton-Cotes formulas as applied to such functions can lead to significant errors. An analogue of Newton-Cotes formulas that is exact for the boundary-layer component is constructed. For the resulting formula, an error estimate that is uniform with respect to the boundary-layer component and its derivatives is obtained. Numerical results that agree with the error estimates are presented. 
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     author = {A. I. Zadorin and N. A. Zadorin},
     title = {Analogue of {Newton-Cotes} formulas for numerical integration of functions with a boundary-layer component},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {368--376},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a3/}
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A. I. Zadorin; N. A. Zadorin. Analogue of Newton-Cotes formulas for numerical integration of functions with a boundary-layer component. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 368-376. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a3/