Equilibrium states for predictor-corrector methods
type: Item
instance of: scholarly article
title: Equilibrium states for predictor-corrector methods
zbMATH Open document ID: 0905.65088
DOI: 10.1016/S0377-0427(97)00239-2
author: Anila Usman
author: George Hall
published in: Journal of Computational and Applied Mathematics
publication date: 1999-01-03T00:00:00Z
review text: Step control (SC) stability is a theory that explains the stepsize patterns of numerical methods with bounded stability regions when they are applied with variable stepsizes to stiff or mildly stiff problems. In the present article, SC-stability is studied for the Adams multistep methods of orders 1 to 4 (in predictor corrector mode). It is shown that most of these methods have difficulties (frequent step rejections) with mildly stiff problems where the dominant eigenvalue of the Jacobian is real. Some numerical experiments illustrate the theoretical results.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 1186862
zbMATH Keywords: predictor-corrector methods
zbMATH Keywords: step control stability
zbMATH Keywords: stability regions
zbMATH Keywords: stepsize control
zbMATH Keywords: stiff problems
zbMATH Keywords: Adams multistep methods
reviewed by: Ernst Hairer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1186862