Geodesic
High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 2, pp. 329-337 
P. W. Hemker; G. I. Shishkin; L. P. Shishkina. High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 44 (2004) no. 2, pp. 329-337. http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_2_a11/
@article{ZVMMF_2004_44_2_a11,
     author = {P. W. Hemker and G. I. Shishkin and L. P. Shishkina},
     title = {High-order accurate decomposition of the {Richardson} method for a singularly perturbed elliptic reaction-diffusion equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {329--337},
     year = {2004},
     volume = {44},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_2_a11/}
}
TY  - JOUR
AU  - P. W. Hemker
AU  - G. I. Shishkin
AU  - L. P. Shishkina
TI  - High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2004
SP  - 329
EP  - 337
VL  - 44
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_2_a11/
LA  - ru
ID  - ZVMMF_2004_44_2_a11
ER  - 
%0 Journal Article
%A P. W. Hemker
%A G. I. Shishkin
%A L. P. Shishkina
%T High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2004
%P 329-337
%V 44
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2004_44_2_a11/
%G ru
%F ZVMMF_2004_44_2_a11

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

[1] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1989 | MR

[2] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989 | MR

[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., 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 Scientific, Singapore, 1996 | MR

[6] Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E., Shishkin G. I., Robust computational techniques for boundary layers, Chapman Hall/CRC Press, Boca Raton, 2000 | MR | Zbl

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

[8] Dulan E., Miller Dzh., Shilders U., Ravnomernye chislennye metody resheniya zadach s pogranichnym sloem, Mir, M., 1983 | MR

[9] Marchuk G. I., Shaidurov V. V., Povyshenie tochnosti reshenii raznostnykh skhem, Nauka, M., 1979 | MR

[10] K. Böhmer, H. J. Stetter (Eds.), Defect correction methods. Theory and applications (Oberwolfach, 1983), Comput. Suppl., 5, Springer, Vienna–New Jork, 1984 | MR

[11] Hemker P. W., Shishkin G. I., Shishkina L. P., “The use of defect correction for the solution of parabolic singular perturbation problems”, Z. Angew. Math. and Mech., 77:1 (1997), 59–74 | DOI | MR | Zbl

[12] Hemker P. W., Shishkin G I., Shishkina L. P., “$\varepsilon$-Uniform schemes with high-order time-accuracy for parabolic singular perturbation problems”, IMA J. Numer. Analys., 20:1 (2000), 99–121 | DOI | MR | Zbl

[13] Shishkin G. I., “Povyshenie tochnosti reshenii raznostnykh skhem dlya parabolicheskikh uravnenii s malym parametrom pri starshei proizvodnoi”, Zh. vychisl. matem. i matem. fiz., 24:6 (1984), 864–875 | MR | Zbl

[14] Shishkin G. I., “Raznostnaya skhema dlya singulyarno vozmuschennogo uravneniya parabolicheskogo tipa s razryvnym granichnym usloviem”, Zh. vychisl. matem. i matem. fiz., 28:11 (1988), 1649–1662 | MR

[15] Shishkin G. I., “Setochnye approksimatsii dlya singulyarno vozmuschennykh ellipticheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 38:12 (1998), 1989–2001 | MR | Zbl

[16] Hemker P. W., Shishkin G. I., Shishkina L. P., “Distributing the numerical solution of parabolic singularly perturbed problems with defect correction over independent processes”, Sibirskii zh. vychisl. matem., 3:3 (2000), 229–258 | Zbl

[17] Hemker P. W., Shishkin G. I., Shishkina L. P., “High-order time-accurate parallel schemes for parabolic singularly perturbed problems with convection”, Computing, 66:2 (2001), 139–161 | DOI | MR | Zbl

[18] Shishkin G. I., “Acceleration of the process of the numerical solution to singularly perturbed boundary value problems for parabolic equations on the basis of parallel computations”, Russ. J. Numer. Analys. and Math. Modelling, 12:3 (1997), 271–291 | DOI | MR | Zbl

[19] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR