Dissipative and Dispersive Properties of Finite Difference Schemes for the Linear Transport Equation on A 4 × 3 Metatemplate

• Published in: Mathematical models and computer simulations Vol. 14; no. 1; pp. 28 - 37
• Main Authors: Goloviznin, V. M., Solovjev, A. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-02-2022; Springer Nature B.V
• Subjects: Approximation; Computational mathematics; Cybernetics; Dispersion; Eigenvalues; Eigenvectors; Finite difference method; Graphical user interface; Information resources; Interface stability; Knowledge bases (artificial intelligence); Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Simulation and Modeling; Surface stability; Transport equations; Websites; difference schemes; high order of approximation; hyperbolic equations; dissipative and dispersive properties; properties of difference schemes
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048222010124

This article is devoted to the presentation of a new information resource on the Internet: a knowledge base on the dissipative and dispersive 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 calculated nodes on three layers by time. An information array containing information on all these schemes is posted on the website of the Laboratory of Industrial Mathematics, Faculty of Computational Mathematics and Cybernetics, Moscow State University at
http://lim.cmc.msu.ru/index.php?id=86
. The information sheet 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 interactively searching for the information using computational templates. As an example, the dissipative and dispersive surfaces of some schemes with different orders of approximation are given.