Richardson’s Third-Order Difference Scheme for the Cauchy Problem in the Case of Transport Equation

The Cauchy problem for the regular transport equation is considered. Using Richardson’s technique, a difference scheme of improved accuracy order on three embedded grids is constructed for this problem. This scheme converges in the maximum norm with the third order of convergence rate.

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2024-10, Vol.64 (10), p.2212-2221
Main Authors: Shishkin, G. I., Shishkina, L. P.
Format: Article
Language:English
Subjects:
Cauchy problems
Computational Mathematics and Numerical Analysis
General Numerical Methods
Mathematics
Mathematics and Statistics
Transport equations
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Summary:The Cauchy problem for the regular transport equation is considered. Using Richardson’s technique, a difference scheme of improved accuracy order on three embedded grids is constructed for this problem. This scheme converges in the maximum norm with the third order of convergence rate.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524701215