Geodesic
A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 99-117.

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

The paper is devoted to construction and justification of a nonuniform difference scheme with fourth order of accuracy for a two-dimensional boundary-value problem for an elliptic equation of second order in a domain with smooth curvilinear boundary. This scheme is called nonuniform because a stencil of difference operator alternates from node to node. In interior nodes a nine-point and standard five-point stencils are used. The special type of stencil is used near the boundary. The paper contains a description for constructing the scheme and for the proof accuracy. Numerical tests confirm the theoretical conclusions about the fourth order of accuracy for the approximate solution. 
@article{SJVM_1998_1_2_a0,
     author = {E. G. Bykova and V. V. Shaidurov},
     title = {A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {99--117},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a0/}
}
TY  - JOUR
AU  - E. G. Bykova
AU  - V. V. Shaidurov
TI  - A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1998
SP  - 99
EP  - 117
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a0/
LA  - ru
ID  - SJVM_1998_1_2_a0
ER  - 
%0 Journal Article
%A E. G. Bykova
%A V. V. Shaidurov
%T A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1998
%P 99-117
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a0/
%G ru
%F SJVM_1998_1_2_a0
E. G. Bykova; V. V. Shaidurov. A~nonuniform difference scheme with fourth order of accuracy in a~domain with smooth boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 99-117. http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a0/

[1] Bykova E. G., Shaidurov V. V., “Dvumernaya neodnorodnaya raznostnaya skhema povyshennogo poryadka tochnosti”, Vychislitelnye tekhnologii. RAN. Sib. otd-nie.— Novosibirsk, 2:5 (1997), 12–25 | MR

[2] Volkov E. A., “Issledovanie odnogo sposoba povysheniya tochnosti metoda setok pri reshenii uravneniya Puassona”, Vychislitelnaya matematika, 1957, no. 1, 62–80 | Zbl

[3] Volkov E. A., “Reshenie zadachi Dirikhle metodom utochnenii raznostyami vysshikh poryadkov, I”, Diff. uravneniya, 1:7 (1965), 946–960 | Zbl

[4] Schortley G. and Weller R., “The numerical solution of the Laplace's equation”, J. Appl. Phys., 9:5 (1938), 334–348 | DOI

[5] Mikeladze Sh. E., “O chislennom integrirovanii uravnenii ellipticheskogo i parabolicheskogo tipa”, Izv. AN SSSR. Ser. matem., 5:1 (1941), 57–73 | MR

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

[7] Rude U., Extrapolation and Related Techniques for Solving Elliptic Equations, Preprint No I-9135, München Technical University, München, 1991

[8] Bykova E. G., Shaidurov V. V., Neodnorodnaya raznostnaya skhema povyshennogo poryadka tochnosti. Odnomernyi illyustrativnyi primer, Preprint No 17, RAN Sib. otd-nie. VTsK, Krasnoyarsk, 1996

[9] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

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