Geodesic
Euler quadrature rule for a function with a boundary layer component on a picewise uniform mesh
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 491-503

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Euler and Gregory quadrature rules for a function with a boundary layer component are investigated. The integrand corresponds to a solution of a singular perturbed problem. It is proved that Euler and Gregory quadrature rules on a mesh, dence in a boundary layer, have a fourth order of an accuracy uniformly in a boundary layer growth of the integrand. Results of numerical experiments are discussed.
Keywords: function, boundary layer, piecewise uniform mesh, uniform accuracy.
Mots-clés : Euler quadrature formula 
@article{SEMR_2013_10_a56,
     author = {A. I. Zadorin and N. A. Zadorin},
     title = {Euler quadrature rule for a function with a boundary layer component on a picewise uniform mesh},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {491--503},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a56/}
}
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A. I. Zadorin; N. A. Zadorin. Euler quadrature rule for a function with a boundary layer component on a picewise uniform mesh. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 491-503. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a56/