Geodesic
Numerical solution of a quasilinear parabolic equation with a boundary layer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 716-726 
I. P. Boglaev. Numerical solution of a quasilinear parabolic equation with a boundary layer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 716-726. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a7/
@article{ZVMMF_1990_30_5_a7,
     author = {I. P. Boglaev},
     title = {Numerical solution of a~quasilinear parabolic equation with a~boundary layer},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {716--726},
     year = {1990},
     volume = {30},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a7/}
}
TY  - JOUR
AU  - I. P. Boglaev
TI  - Numerical solution of a quasilinear parabolic equation with a boundary layer
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 716
EP  - 726
VL  - 30
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a7/
LA  - ru
ID  - ZVMMF_1990_30_5_a7
ER  - 
%0 Journal Article
%A I. P. Boglaev
%T Numerical solution of a quasilinear parabolic equation with a boundary layer
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 716-726
%V 30
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a7/
%G ru
%F ZVMMF_1990_30_5_a7

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

To solve a quasilinear parabolic equation with small parameter multiplying the derivatives with respect to the spatial variables, a numerical method is constructed with an estimate of the error, which is uniform with respect to the parameter. The construction of a nonlinear difference scheme is based on the method of straight lines and on the application of exact systems to one-dimensional problems. The computational mesh is chosen so that its density increases in a suitable way in the neighbourhood of the boundary. We propose that the nonlinear scheme be solved by an iterative algorithm, which converges uniformly with respect to the small parameter.

[1] Trenogin V. A., “Ob asimptotike resheniya pochti lineinykh parabolicheskikh uravnenii s parabolicheskim pogransloem”, Uspekhi matem. nauk, 16:I (97) (1961), 163–169 | MR | Zbl

[2] Boglaev I. P. i dr., O vnutrennem okislenii dvukhfaznykh splavov, Preprint, IFTT AH CSSR, M., 1978

[3] Bakhvalov N. S., “K optimizatsii metodov resheniya kraevykh zadach pri nalichii pogranichnogo sloya”, Zh. vychisl. matem. i matem. fiz., 9:4 (1969), 841–859 | Zbl

[4] Shishkin G. I., “Raznostnaya skhema na neravnomernoi setke dlya differentsialnogo uravneniya s malym parametrom pri starshei proizvodnoi”, Zh. vychisl. matem. i matem. fiz., 23:3 (1983), 609–619 | MR | Zbl

[5] Makarov V. L., Samarskii A. A., “Primenenie tochnykh raznostnykh skhem k otsenke skorosti skhodimosti metoda pryamykh”, Zh. vychisl. matem. i matem. fiz., 20:2 (1980), 371–387 | MR | Zbl

[6] Boglaev I. P., “Priblizhennoe reshenie nelineinoi kraevoi zadachi s malym parametrom pri starshei proizvodnoi”, Zh. vychisl. matem. i matem. fiz., 24:11 (1984), 1649–1656 | MR | Zbl

[7] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[8] Boglaev I. P., O raznostnom metode resheniya kraevoi zadachi s malym parametrom pri starshei proizvodnoi, Preprint, IFTT AN SSSR, M., 1981 | MR