Geodesic
Quadrature formulas for functions with a boundary-layer component
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1952-1962 
A. I. Zadorin; N. A. Zadorin. Quadrature formulas for functions with a boundary-layer component. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1952-1962. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a1/
@article{ZVMMF_2011_51_11_a1,
     author = {A. I. Zadorin and N. A. Zadorin},
     title = {Quadrature formulas for functions with a~boundary-layer component},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1952--1962},
     year = {2011},
     volume = {51},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a1/}
}
TY  - JOUR
AU  - A. I. Zadorin
AU  - N. A. Zadorin
TI  - Quadrature formulas for functions with a boundary-layer component
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1952
EP  - 1962
VL  - 51
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a1/
LA  - ru
ID  - ZVMMF_2011_51_11_a1
ER  - 
%0 Journal Article
%A A. I. Zadorin
%A N. A. Zadorin
%T Quadrature formulas for functions with a boundary-layer component
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1952-1962
%V 51
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a1/
%G ru
%F ZVMMF_2011_51_11_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

Quadrature formulas for one-variable functions with a boundary-layer component are constructed and studied. It is assumed that the integrand can be represented as the sum of a regular and a boundary-layer component, the latter having high gradients that reduce the accuracy of classical quadrature formulas, such as the trapezoidal and Simpson rules. The formulas are modified so that their error is independent of the gradients of the boundary-layer component. Results of numerical experiments are presented.

[1] Kantorovich L. V., “O priblizhennom vychislenii nekotorykh tipov opredelennykh integralov i drugikh primeneniyakh metoda vydeleniya osobennostei”, Matem. sb., 41:2 (1934), 235–244 | MR

[2] Berezin I. S., Zhidkov N. P., Metody vychislenii, Nauka, M., 1966

[3] Bakhvalov N. S., Chislennye metody, Nauka, M., 1975

[4] Shishkin G. I., Setochnye approksimatsii singulyarno vozmuschennykh ellipticheskikh i parabolicheskikh uravnenii, UrO RAN, Ekaterinburg, 1992

[5] Miller J. J. H., O'Riordan E., Shishkin G. I., Fitted numerical methods for singular perturbation problems, World Scient., Singapure, 1996 | MR

[6] Kellogg R. B., Tsan A., “Analysis of some difference approximations for a singular perturbation problems without turning points”, Math. Comput., 32 (1978), 1025–1039 | DOI | MR | Zbl

[7] Zadorin A. I., “Metod interpolyatsii dlya zadachi s pogranichnym sloem”, Sibirskii zh. vychisl. matem., 10:3 (2007), 267–275

[8] Zadorin A. I., “Interpolation method for a function with a singular component”, Lect. Notes in Comput. Sci., 5434, Springer, Berlin, 2009, 612–619 | DOI | Zbl

[9] Zadorin A. I., Zadorin N. A., “Splain-interpolyatsiya na ravnomernoi setke funktsii s pogransloinoi sostavlyayuschei”, Zh. vychisl. matem. i matem. fiz., 50:2 (2010), 221–233 | MR | Zbl