Geodesic
Dissipative and dispersive properties of finite difference schemes for the linear transport equation on the $4\times3$ meta-template
Matematičeskoe modelirovanie, Tome 33 (2021) no. 6, pp. 45-58

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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. 
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     author = {V. M. Goloviznin and A. V. Solovjev},
     title = {Dissipative and dispersive properties of finite difference schemes for the linear transport equation on the $4\times3$ meta-template},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {45--58},
     publisher = {mathdoc},
     volume = {33},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_6_a3/}
}
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V. M. Goloviznin; A. V. Solovjev. Dissipative and dispersive properties of finite difference schemes for the linear transport equation on the $4\times3$ meta-template. Matematičeskoe modelirovanie, Tome 33 (2021) no. 6, pp. 45-58. http://geodesic.mathdoc.fr/item/MM_2021_33_6_a3/