Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
type: Item
instance of: scholarly article
title: Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
zbMATH Open document ID: 0886.65099
author: Bernhard Rupp
published in: Journal of Computational Physics
publication date: 1998-04-14T00:00:00Z
review text: The authors introduce a new kind of numerical schemes, designed for both monoticity and accuracy properties. These schemes involve piecewise polynomial solutions, together with an accurate interface formula and Runge-Kutta time stepping. They are presented in details concerning the advection equation with constant speed. In this case, they are proved to be monoticity preserving as well as high-order accurate. Then they are extended to the Euler equations in 1-D and 2-D. Several numerical experiments are provided, in which they compare favorably with ENO and weighted ENO schemes.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 1066703
zbMATH Keywords: monotonicity-preserving schemes
zbMATH Keywords: Euler equations
zbMATH Keywords: numerical examples
zbMATH Keywords: comparison of methods
zbMATH Keywords: Runge-Kutta time stepping
zbMATH Keywords: weighted ENO schemes
zbMATH Keywords: advection equation
MaRDI profile type: Publication
full work available at URL: jcph.1997.5745
OpenAlex ID: W2109614403
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DOI: 10.1006/JCPH.1997.5745
description: scientific article; zbMATH DE number 1066703