Algebraic stability and the existence of solutions of implicit Runge- Kutta equations
type: Item
instance of: scholarly article
title: Algebraic stability and the existence of solutions of implicit Runge- Kutta equations
zbMATH Open document ID: 0584.65047
DOI: 10.1007/BF01934382
author: G. J. Cooper
published in: BIT
publication date: 1985-01-01T00:00:00Z
review text: It is shown that an irreducible Runge-Kutta method whose Runge-Kutta matrix, A, is nonsingular is (k,\(\ell)\)-algebraically stable on (- \(\infty,a)\), \(a>0\) with \(k(0)=1\) iff the method is algebraically stable and there exists a diagonal matrix \(R>0\) such that \(RA+A^ TR>0\). This last condition guarantees the existence of unique solutions for the internal approximations when a Runge-Kutta method is applied to a monotonic problem.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3936404
zbMATH Keywords: algebraic stability
zbMATH Keywords: irreducible Runge-Kutta method
reviewed by: Kevin Burrage
MaRDI profile type: Publication
cites work: Stability Criteria for Implicit Runge–Kutta Methods
cites work: Non-linear stability of a general class of differential equation methods
cites work: A Generalization of Algebraic Stability for Runge--Kutta Methods
cites work: Sur la B-stabilité des méthodes de Runge-Kutta
cites work: On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods
cites work: Reducibility and contractivity of Runge-Kutta methods revisited
description: scientific article; zbMATH DE number 3936404