Geodesic
About a local grid method of a solution of Laplace’s equation in the infinite rectangular cylinder
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 1, pp. 97-104 
E. A. Volkov. About a local grid method of a solution of Laplace’s equation in the infinite rectangular cylinder. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 1, pp. 97-104. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_1_a8/
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     title = {About a local grid method of a solution of {Laplace{\textquoteright}s} equation in the infinite rectangular cylinder},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Dirichlet problem for Laplace’s equation on an infinite rectangular cylinder is considered. The main goal is to develop a grid method for finding an approximate solution of the Dirichlet problem in a finite part of the infinite cylinder without solving the entire problem. The underlying idea is that the influence of the boundary values on the solution at a fixed point of the domain decreases as the boundary moves away.

[1] Volkov E.A., “O reshenii metodom setok uravneniya Laplasa v beskonechnom pryamougolnom tsilindre pri periodicheskikh granichnykh usloviyakh”, Tr. MI RAN, 269, M., 2010, 63–70 | MR | Zbl

[2] Mikhailov V.P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983

[3] Samarskii A.A., Andreev V.B., Raznostnye metody dlya ellipticheskikh uravnenii, Nauka, M., 1976