Explicit general linear methods with inherent Runge--Kutta stability
type: Item
instance of: scholarly article
title: Explicit general linear methods with inherent Runge--Kutta stability
zbMATH Open document ID: 1016.65049
DOI: 10.1023/A:1021195804379
author: Yanyan Li
published in: Numerical Algorithms
publication date: 2003-03-10T00:00:00Z
review text: The goal of the paper is the construction of a new class of practically useful general linear methods for the numerical solution of non-stiff ordinary differential equations. The methods are generated in a way that guarantees that their stability regions are large (indeed, identical to the stability regions of certain Runge-Kutta methods). The stage order of the new methods is high, thus allowing efficient error estimates and the construction of high order interpolants. The main properties of the rules are described. A section of the paper is devoted to the question of finding the methods explicitly. Some special cases are given in detail. Numerical experiments indicate the quality of the new methods.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1879378
zbMATH Keywords: general linear methods
zbMATH Keywords: inherent Runge-Kutta stability
zbMATH Keywords: Nordsieck form
zbMATH Keywords: stability regions
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: error estimates
zbMATH Keywords: numerical experiments
describes a project that uses: RADAU
describes a project that uses: DESIRE
MaRDI profile type: Publication
full work available at URL: a:1021195804379
OpenAlex ID: W1633806305
description: scientific article; zbMATH DE number 1879378