Two barriers on strong-stability-preserving time discretization methods
type: Item
instance of: scholarly article
title: Two barriers on strong-stability-preserving time discretization methods
zbMATH Open document ID: 1003.65107
DOI: 10.1023/A:1015156832269
author: Steven J. Ruuth
author: R. J. Spiteri
published in: Journal of Scientific Computing
publication date: 2002-08-20T00:00:00Z
review text: The authors study systems of ordinary differential equations obtained from the methods of lines applied to the hyperbolic conservation law \[ u_t+ f(u)_x= 0 \] with appropriate initial and boundary conditions. They note that the usual linear stability analysis in not effective for schemes of problems having discontinuous or shock-like solutions. In such cases strong-stability-preserving (SSP) methods are needed. The authors discuss Runge-Kutta type methods SSPRK having positive coefficients. The main results of the paper concern the conditions which a Runge-Kutta method with positive coefficients have to fulfill to be SSP. These refer to the coefficients and the order of the method which cannot be superior to \(4\).
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1784232
zbMATH Keywords: strong stability preserving
zbMATH Keywords: total variation diminishing
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: high-order accuracy
zbMATH Keywords: time discretization
zbMATH Keywords: methods of lines
zbMATH Keywords: hyperbolic conservation law
zbMATH Keywords: discontinuous or shock-like solutions
MaRDI profile type: Publication
full work available at URL: a:1015156832269
OpenAlex ID: W1549623142
description: scientific article; zbMATH DE number 1784232