Strong stability preserving explicit Runge-Kutta methods of maximal effective order
type: Item
instance of: scholarly article
zbMATH Open document ID: 1278.65116
DOI: 10.1137/120884201
author: Yiannis Hadjimichael
author: Colin B. Macdonald
author: David I. Ketcheson
author: James H. Verner
published in: SIAM Journal on Numerical Analysis
publication date: 2013-10-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1207.2902
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 6219398
zbMATH Keywords: monotonicity
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: time integration
zbMATH Keywords: high-order accuracy
zbMATH Keywords: TVD discretization
zbMATH Keywords: method of lines
zbMATH Keywords: strong stability preserving time discretizations
zbMATH Keywords: effective order of accuracy
zbMATH Keywords: starting and stopping methods
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
OpenAlex ID: W2126193525
arXiv ID: 1207.2902
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title: Strong stability preserving explicit Runge-Kutta methods of maximal effective order
review text: The authors use the theory of strong stability preserving (SSP) time discretizations with Butcher's algebraic interpretation of order to construct explicit SSP Runge-Kutta schemes with an effective order of accuracy. These methods, when accompanied by starting and stopping methods, attain an order of accuracy higher than their (classical) order. The authors propose a new choice of starting and stopping methods to allow the overall procedure to be SSP. Moreover, they prove that explicit Runge-Kutta methods with strictly positive weights have at most effective order four. Numerical experiments demonstrate the validity of these methods in practice.
reviewed by: Qin Meng Zhao
description: scientific article; zbMATH DE number 6219398