Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration
type: Item
instance of: scholarly article
title: Stability analysis for linear discretisations of the advection equation with Runge-Kutta time integration
zbMATH Open document ID: 1149.65064
author: Michael Baldauf
published in: Journal of Computational Physics
publication date: 2008-07-21T00:00:00Z
review text: The aim of the paper is the systematic calculation of stability limits for Runge-Kutta methods up to 7th order in combination with upwind or centered difference schemes up to 6th order, for the linear advection problem. The first section represents an introduction in nature. The second section gives a linear view to explicit Runge-Kutta schemes, showing that it is not necessary to make a distinction between different Runge-Kutta methods of a certain order. The author defines a very large class of Runge-Kutta methods, called Linear Case-RK (LC-RK), with exactly the same linear stability properties. In the third section the stability limits for LC-RK methods for different linear, spatial discretisation of the one-dimensional advection operator are calculated. The fourth section contains some numerical experiments carried out to highlight the practical meaning of the stability limits found in the previous section. In the fifth section the author presents an extension to the space splitted multi-dimensional case. Thus, he considers the two-dimensional advection equation. The main conclusions about the efficiency of these schemes are within the last section.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 5303110
zbMATH Keywords: linear advection
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: linear stability
zbMATH Keywords: von-Neumann stability
reviewed by: Romulus Militaru
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: j.jcp.2008.03.025
OpenAlex ID: W2073281758
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DOI: 10.1016/J.JCP.2008.03.025
description: scientific article; zbMATH DE number 5303110