Cubature formulas for a two-variable function with boundary-layer components
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1997-2007
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Cubature formulas for evaluating the double integral of a two-variable function with boundary-layer components are constructed and studied. Because of the boundary-layer components, the cubature formulas based on Newton–Cotes formulas become considerably less accurate. Analogues of the trapezoidal and Simpson rules that are exact for the boundary-layer components are constructed. Error estimates for the constructed formulas are derived that are uniform in the gradients of the integrand in the boundary layers.
@article{ZVMMF_2013_53_12_a4,
author = {A. I. Zadorin},
title = {Cubature formulas for a two-variable function with boundary-layer components},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1997--2007},
publisher = {mathdoc},
volume = {53},
number = {12},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a4/}
}
TY - JOUR AU - A. I. Zadorin TI - Cubature formulas for a two-variable function with boundary-layer components JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2013 SP - 1997 EP - 2007 VL - 53 IS - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a4/ LA - ru ID - ZVMMF_2013_53_12_a4 ER -
%0 Journal Article %A A. I. Zadorin %T Cubature formulas for a two-variable function with boundary-layer components %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2013 %P 1997-2007 %V 53 %N 12 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a4/ %G ru %F ZVMMF_2013_53_12_a4
A. I. Zadorin. Cubature formulas for a two-variable function with boundary-layer components. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1997-2007. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a4/