This article is cited in 1 paper

General numerical methods

An improved difference scheme for the Cauchy problem in the case of a transport equation

G. I. Shishkin, L. P. Shishkina

Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, 620108, Yekaterinburg, Russia

Abstract: The Cauchy problem for the regular transport equation is considered. The Richardson technique is used to construct an improved difference scheme that converges in the maximum norm with the second order of convergence.

Key words: transport equation, Cauchy problem, standard difference scheme, uniform grid, residual, expansion of residual, monotonicity of differential and grid problems, Richardson technique, improved difference scheme, convergence in the maximum norm.

UDC: 519.63

Received: 04.04.2023
Revised: 04.04.2023
Accepted: 28.04.2023

DOI: 10.31857/S0044466923080136

 English version: Computational Mathematics and Mathematical Physics, 2023, 63:8, 1401–1407

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