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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 6, Pages 859–872
DOI: https://doi.org/10.7868/S0044466918060017
(Mi zvmmf10699)
 

This article is cited in 2 scientific papers (total in 2 papers)

Difference schemes in the undetermined coefficient space and dual problems of linear programming

A. I. Lobanov

Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia
Citations (2)
References:
Abstract: Using properties of the difference schemes approximating a one-dimensional transport equation as an example, it is shown that optimization of the properties of difference schemes based on the analysis in the space of undetermined coefficients and optimization of these properties based on the method of parametric correction are dual problems. Hybrid difference schemes for the linear transport equation are built as solutions to dual linear programming problems. It is shown that Godunov’s theorem follows from the linear program optimality criterion as one of the complementary slackness conditions. A family of hybrid difference schemes is considered. It is shown that Fedorenko’s hybrid difference scheme is obtained by solving the dual linear programming problem.
Key words: linear transport equation, difference scheme, Fedorenko's hybrid scheme, linear programming problem, complementary slackness conditions, monotonic schemes, Lagrange multipliers, Godunov's theorem.
Received: 30.05.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 6, Pages 827–839
DOI: https://doi.org/10.1134/S0965542518060088
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: A. I. Lobanov, “Difference schemes in the undetermined coefficient space and dual problems of linear programming”, Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018), 859–872; Comput. Math. Math. Phys., 58:6 (2018), 827–839
Citation in format AMSBIB
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Abstract page:281
    References:38
     
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