Geodesic
An implicit iterative method for numerical solution
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 95-106.

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

We propose and study some implicit gradient two-layer iterative method for numerical solution of the Cauchy problem for elliptic equations. The results of computational experiments are presented.
Keywords: inverse problem, Cauchy problem, implicit two-layer iterative method, difference scheme, variable separation method.
Mots-clés : elliptic equations 
@article{SJIM_2019_22_4_a9,
     author = {S. B. Sorokin},
     title = {An implicit iterative method for numerical solution},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {95--106},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a9/}
}
TY  - JOUR
AU  - S. B. Sorokin
TI  - An implicit iterative method for numerical solution
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2019
SP  - 95
EP  - 106
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a9/
LA  - ru
ID  - SJIM_2019_22_4_a9
ER  - 
%0 Journal Article
%A S. B. Sorokin
%T An implicit iterative method for numerical solution
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2019
%P 95-106
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a9/
%G ru
%F SJIM_2019_22_4_a9
S. B. Sorokin. An implicit iterative method for numerical solution. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 4, pp. 95-106. http://geodesic.mathdoc.fr/item/SJIM_2019_22_4_a9/

[1] A. N. Tikhonov, V. Ya. Arsenin, Metody resheniya nekorrektnykh zadach, Nauka, M., 1979

[2] S. I. Kabanikhin, A. L. Karchevsky, “Optimizational method for solving the Cauchy problem for an elliptic equation”, J. Inverse Ill-Posed Probl., 3:1 (1995), 21–46 | DOI | MR | Zbl

[3] S. I. Kabanikhin, Obratnye i nekorrektnye zadachi, Sibirskoe nauchnoe izd-vo, Novosibirsk, 2009

[4] A. A. Samarskii, E. S. Nikolaev, Metody resheniya setochnykh uravnenii, Nauka, M., 1978

[5] A. A. Samarskii, V. B. Andreev, Raznostnye metody dlya ellipticheskikh uravnenii, Nauka, M., 1979

[6] S. B. Sorokin, “Ekonomichnyi pryamoi metod chislennogo resheniya zadachi Koshi dlya uravneniya Laplasa”, Sib. zhurn. vychisl. matematiki, 22:1 (2019), 99–117 | MR

[7] A. L. Karchevskii, “Korrektnaya skhema deistvii pri chislennom reshenii obratnoi zadachi optimizatsionnym metodom”, Sib. elektron. mat. izv., 5 (2008), 609–619