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Mathematical Models and Computer Simulations

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01-11-2019

Cabaret Difference Scheme with Improved Dispersion Properties

Authors: A. I. Sukhinov, A. E. Chistyakov

Published in: Mathematical Models and Computer Simulations | Issue 6/2019

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Abstract

A difference scheme for the transfer problem, constructed as a linear combination of the Cabaret scheme and the central difference scheme, is proposed. The stability and dispersion properties of the scheme are studied. It is shown that the constructed scheme has the best dispersion properties for high-frequency harmonics at small Courant numbers compared with the known Cabaret scheme for the transport equation. A comparison is made of the errors of this scheme and the two-parameter third-order difference accuracy scheme based on the numerical experiments on the previously used test problem sets. It is shown that in the normal grid space L₁ the developed scheme has smaller errors and also uses a more compact template (in calculating the inode the node values i – 1, i, and i + 1 are used), and the transition to the next time layer is carried out for a smaller number of arithmetic operations.

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Title: Cabaret Difference Scheme with Improved Dispersion Properties
Authors: A. I. Sukhinov
A. E. Chistyakov
Publication date: 01-11-2019
Publisher: Pleiades Publishing
Published in: Mathematical Models and Computer Simulations / Issue 6/2019
Print ISSN: 2070-0482
Electronic ISSN: 2070-0490
DOI: https://doi.org/10.1134/S207004821906019X

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