Difference Schemes in the Undetermined Coefficient Space and Dual Problems of Linear Programming

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...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2018-06, Vol.58 (6), p.827-839
Main Author: Lobanov, A. I.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Linear programming
Mathematics
Mathematics and Statistics
Optimality criteria
Optimization
Properties (attributes)
Transport equations
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542518060088