ARK methods up to order five
type: Item
instance of: scholarly article
title: ARK methods up to order five
zbMATH Open document ID: 0907.65069
DOI: 10.1023/A:1016640625396
published in: Numerical Algorithms
publication date: 1999-03-04T00:00:00Z
review text: The properties of almost Runge-Kutta (ARK) methods are investigated and methods with \(s\) (stages in each step) \(=p\) (the order of the method) are derived for all orders up to five. Methods with \(s= p+1\) have also been explored and are represented in the single case \(p= 5\). The author discusses the conditions: a) for an ARK to have a specific order; b) for one of these methods to have linear stability properties exactly as for a classical Runge-Kutta method. Results of numerical experiments with the new methods are presented.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1204230
zbMATH Keywords: numerical examples
zbMATH Keywords: almost Runge-Kutta methods
zbMATH Keywords: order
zbMATH Keywords: linear stability
author: J. C. Butcher
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
full work available at URL: a:1016640625396
OpenAlex ID: W2025876243
description: scientific article; zbMATH DE number 1204230