Algebraically stable general linear methods and the \(G\)-matrix
type: Item
instance of: scholarly article
title: Algebraically stable general linear methods and the \(G\)-matrix
zbMATH Open document ID: 1167.65042
author: L. L. Hewitt
author: Adrian T. Hill
published in: BIT
publication date: 2009-04-29T00:00:00Z
review text: The authors discuss the algebraic stability of general linear methods, which governs long-time dynamics for dissipative systems and represents a stronger requirement than A-stability. The condition is reformulated in a modified form and connected to a branch of control theory concerned with the discrete algebraic Riccati equation. It is shown that the main condition for algebraic stability can be reformulated as an equation rather than an inequality with little loss of generality. For the construction of methods, the authors propose to first impose stability and subsequently satisfy the order conditions. The theoretical results are exploited to construct several new example methods with two steps and two stages.
reviewed by: Othmar Koch
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 5549597
zbMATH Keywords: general linear methods
zbMATH Keywords: algebraic stability
zbMATH Keywords: order conditions
zbMATH Keywords: discrete algebraic Riccati equation
zbMATH Keywords: numerical examples
zbMATH Keywords: dissipative systems
MaRDI profile type: Publication
full work available at URL: s10543-008-0207-7
OpenAlex ID: W2092615568
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DOI: 10.1007/S10543-008-0207-7
description: scientific article; zbMATH DE number 5549597