\(A_ 0\)-stable linear multistep formulas of the \(\alpha\)-type
type: Item
instance of: scholarly article
title: \(A_ 0\)-stable linear multistep formulas of the \(\alpha\)-type
zbMATH Open document ID: 0626.65070
DOI: 10.1007/BF01937360
author: Gary K. Rockswold
published in: BIT
publication date: 1987-01-01T00:00:00Z
review text: This paper examines the \(A_ 0\)-stability of the k-step order k linear multistep method of the form \[ y_{n+k}-\alpha y_{n+k-1}+(\alpha - 1)y_{n+k-2}=h\sum^{k}_{i=0}\beta_ iy'_{n+i}. \] All \(A_ 0\)- stable methods of order 4 or less are found and it is shown that there are no \(A_ 0\)-stable k-step methods of order 5 or more of the above form.
reviewed by: Kevin Burrage
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4018269
zbMATH Keywords: alpha type methods
zbMATH Keywords: A-zero-stability
zbMATH Keywords: linear multistep method
MaRDI profile type: Publication
cites work: Algorithms for Classical Stability Problems
cites work: $A_0 $-Stable Formulas of Adams Type
cites work: Q5719651
cites work: Low-order \(A_0\)-stable Adams-type correctors
cites work: A note on unconditionally stable linear multistep methods
cites work: Zero-stability properties of the three-ordinate variable stepsize variable formula methods
full work available at URL: https://doi.org/10.1007/bf01937360
OpenAlex ID: W2020814185
description: scientific article; zbMATH DE number 4018269