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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2019, Volume 22, Number 1, Pages 99–117
DOI: https://doi.org/10.15372/SJNM20190107 (Mi sjvm703) 		 
This article is cited in 11 scientific papers (total in 11 papers)

An efficient direct method for the numerical solution to the Cauchy problem for the Laplace equation

S. B. Sorokinab

a Novosibirsk State University, st. Pirogova 2, Novosibirsk, 630090, Russia
b Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Akad. Lavrentjeva 6, Novosibirsk, 630090, Russia
Full-text PDF (4745 kB) Citations (11)
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DOI: https://doi.org/10.15372/SJNM20190107
Abstract: One of widespread approaches to solving the Cauchy problem for the Laplace equation is to reduce it to the inverse problem. As a rule, an iterative procedure to solve the latter is used. In this study, an efficient direct method for the numerical solution of the inverse problem in the rectangular form is described. The main idea is based on the expansion of the desired solution with respect to a basis consisting of eigenfunctions of a difference analogue of the Laplace operator.
Key words: Cauchy problem for Laplace equation, inverse problem, numerical solution, efficient direct method.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by Basic Research Program of the Department of Mathematical Sciences of the Russian Academy of Sciences on Modern Computational and Informational Technologies for Large Problems and RAS Presidium under Program on Intelligent Information Technologies, Mathematical Modeling, System Analysis, and Automatization.
Received: 28.12.2017
Revised: 06.06.2018
Accepted: 05.10.2018
English version:
Numerical Analysis and Applications, 2019, Volume 12, Issue 1, Pages 87–103
DOI: https://doi.org/10.1134/S1995423919010075
Bibliographic databases:
Document Type: Article
UDC: 519.632
Language: Russian
Citation: S. B. Sorokin, “An efficient direct method for the numerical solution to the Cauchy problem for the Laplace equation”, Sib. Zh. Vychisl. Mat., 22:1 (2019), 99–117; Num. Anal. Appl., 12:1 (2019), 87–103
Citation in format AMSBIB
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