On implicity Runge-Kutta methods with a stability function having distinct real poles
type: Item
instance of: scholarly article
title: On implicity Runge-Kutta methods with a stability function having distinct real poles
zbMATH Open document ID: 0673.65050
DOI: 10.1007/BF01932708
author: Stephen L. Keeling
published in: BIT
publication date: 1989-01-01T00:00:00Z
review text: As distinct from the situation in serial machines, where singly implicit Runge-Kutta (RK) methods are computationally more advantageous than other implicit RK formulae, a parallel environment may suggest the use of RK methods whose stability function has pairwise distinct poles. These are called multiply implicit RKs (MIRKs). Here the attention is concentrated on MIRKs with real poles (real MIRKs). Complex poles would allow a higher classical order but not a higher stiff order. It is proved that a real MIRK with q stages and order \(q+1\) cannot be \(A\)-stable unless \(q=1,2,3,5\). The author construct for each \(q\) a \(q\)-stage, \(A_ 0\)-stable, order \(q+1\) real MIRK and a q-stage, I-stable, order \(q\) real MIRK. Algebraically stable real MIRKs are also given.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4102413
zbMATH Keywords: order reduction
zbMATH Keywords: parallel computation
zbMATH Keywords: \(A\)-stability
zbMATH Keywords: \(A\)-stable methods
zbMATH Keywords: multiply
zbMATH Keywords: implicit methods
zbMATH Keywords: real-pole sandwich
zbMATH Keywords: singly implicit Runge-Kutta
zbMATH Keywords: methods
zbMATH Keywords: stability
reviewed by: Jesús María Sanz-Serna
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01932708
OpenAlex ID: W2042156583
description: scientific article; zbMATH DE number 4102413