Solving implicit equations arising from Adams-Moulton methods
type: Item
instance of: scholarly article
title: Solving implicit equations arising from Adams-Moulton methods
zbMATH Open document ID: 1008.65047
DOI: 10.1023/A:1021951025649
author: Tian Min Han
author: Yuhuan Han
published in: BIT
publication date: 2002-09-19T00:00:00Z
review text: This paper gives a new method which uses functional iteration to solve the implicit equations generated by the Adams-Moulton method. The method depends on a parameter, \(\varepsilon\) which shifts the centre of the convergence circle for the iteration to \((-h/\varepsilon,0)\) and increases the radius of convergence by \(h/\varepsilon\). For a fixed number of iterations, the smaller the \(\varepsilon\) the better the stability properties but the worse the error behaviour. Numerical comparisons indicate the potential of this approach.
reviewed by: Kevin Burrage
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 1803313
zbMATH Keywords: numerical examples
zbMATH Keywords: functional iteration
zbMATH Keywords: Adams-Moulton method
zbMATH Keywords: convergence
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: a:1021951025649
OpenAlex ID: W160670252
description: scientific article; zbMATH DE number 1803313