Geodesic
Simpson rule and its modifications for a function with a boundary layer component
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 258-267

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Quadrature formulas for a function with a boundary layer component are investigated. An application of Simpson rule on an uniform mesh for the integration of such function leads to significant errors. Two approaches to increase the accuracy are investigated: the fitting of Simpson rule to a boundary layer component and using Simpson rule on Shishkin mesh. Results of numerical experiments are discussed.
Keywords: definite integral, boundary layer component, Simpson rule, Shishkin mesh
Mots-clés : singular perturbation, modification, error estimation. 
@article{SEMR_2014_11_a67,
     author = {A. I. Zadorin and N. A. Zadorin},
     title = {Simpson rule and its modifications for a function with a boundary layer component},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {258--267},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a67/}
}
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A. I. Zadorin; N. A. Zadorin. Simpson rule and its modifications for a function with a boundary layer component. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 258-267. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a67/