Abstract:
The article is devoted to the presentation of a new information resource on the Internet — a knowledge base on the dissipative and dispersion properties of difference schemes for
the simplest linear transport equation, covering 2113 schemes from the first order of
approximation to the tenth, which can be obtained on a computational template of four
computational nodes on three layers according to time. An information array containing
passports of all these schemes is posted on the website of the Industrial Mathematics
Laboratory of the VMK MSU at http://lim.cmc.msu.ru/index.php?id=86. The passport of
the difference scheme contains the coefficients of the characteristic equations, the
stability region, and dissipative and dispersive surfaces. The friendly graphical user
interface allows you to interactively search for passports using computational templates.
As an example, the dissipative and dispersion surfaces of some schemes with different
orders of approximation are given.
Keywords:
hyperbolic equations, properties of difference schemes, dissipative and
dispersion properties, difference schemes, high order of approximation.
Citation:
V. M. Goloviznin, A. V. Solovjev, “Dissipative and dispersive properties of finite difference schemes for the linear transport equation on the 4×3 meta-template”, Mat. Model., 33:6 (2021), 45–58; Math. Models Comput. Simul., 14:1 (2022), 28–37
\Bibitem{GolSol21}
\by V.~M.~Goloviznin, A.~V.~Solovjev
\paper Dissipative and dispersive properties of finite difference schemes for the linear transport equation on the $4\times3$ meta-template
\jour Mat. Model.
\yr 2021
\vol 33
\issue 6
\pages 45--58
\mathnet{http://mi.mathnet.ru/mm4294}
\crossref{https://doi.org/10.20948/mm-2021-06-04}
\transl
\jour Math. Models Comput. Simul.
\yr 2022
\vol 14
\issue 1
\pages 28--37
\crossref{https://doi.org/10.1134/S2070048222010124}
Linking options:
https://www.mathnet.ru/eng/mm4294
https://www.mathnet.ru/eng/mm/v33/i6/p45
This publication is cited in the following 2 articles:
I. B. Petrov, V. I. Golubev, A. V. Shevchenko, A. Sharma, “Three-dimensional grid-characteristic schemes of high order of approximation”, Dokl. Math., 110:3 (2024), 457–463
I. B. Petrov, V. I. Golubev, A. V. Shevchenko, I. S. Nikitin, “About the boundary condition approximation in the higher-order grid-characteristic schemes”, Dokl. Math., 108:3 (2023), 466–471
Citation in format AMSBIB
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