Geodesic
Method of interpolation for a~boundary layer problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 3, pp. 267-275.

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

A singularly perturbed boundary value problem for a second order ordinary differential equation is considered. It is assumed that the solution is found at the nodes of a uniform or nonuniform mesh. An interpolation method taking into account the boundary layer part of the solution is proposed. Using the constructed interpolation function, we find the derivative of the solution with an accuracy uniform with respect to a parameter at any point of the interval. 
@article{SJVM_2007_10_3_a3,
     author = {A. I. Zadorin},
     title = {Method of interpolation for a~boundary layer problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {267--275},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2007_10_3_a3/}
}
TY  - JOUR
AU  - A. I. Zadorin
TI  - Method of interpolation for a~boundary layer problem
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2007
SP  - 267
EP  - 275
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2007_10_3_a3/
LA  - ru
ID  - SJVM_2007_10_3_a3
ER  - 
%0 Journal Article
%A A. I. Zadorin
%T Method of interpolation for a~boundary layer problem
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2007
%P 267-275
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2007_10_3_a3/
%G ru
%F SJVM_2007_10_3_a3
A. I. Zadorin. Method of interpolation for a~boundary layer problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 3, pp. 267-275. http://geodesic.mathdoc.fr/item/SJVM_2007_10_3_a3/

[1] Ilin A. M., “Raznostnaya skhema dlya differentsialnogo uravneniya s malym parametrom pri starshei proizvodnoi”, Matem. zametki, 6:2 (1969), 237–248

[2] Bakhvalov N. S., “K optimizatsii metodov resheniya kraevykh zadach pri nalichii pogranichnogo sloya”, Zhurn. vychisl. matem. i mat. fiziki, 9:4 (1969), 841–890

[3] Shishkin G. I., Setochnye approksimatsii singulyarno vozmuschennykh ellipticheskikh i parabolicheskikh uravnenii, Izd-vo UrO RAN, Ekaterinburg, 1992

[4] Kellogg R. B., Tsan A., “Analysis of some difference approximations for a singular perturbation problems without turning points”, Math. Comput., 32:144 (1978), 1025–1039 | DOI | MR | Zbl

[5] Miller J. J. H., O'Riordan E., Shishkin G. I., Fitted Numerical Methods for Singular Perturbation Problems, World Scientific, Singapore, 1996 | MR