Remarks on Picard-Lindelöf iteration
type: Item
instance of: scholarly article
title: Remarks on Picard-Lindelöf iteration
zbMATH Open document ID: 0673.65037
DOI: 10.1007/BF01952687
author: Olavi Nevanlinna
published in: BIT
publication date: 1989-01-01T00:00:00Z
review text: The author discusses the Picard-Lindelöf iteration for systems of autonomous linear ordinary differential equations on finite intervals and its various numerical variants. The discussion presented assumes that the coupling terms are of moderate size compared with the low time scales in the problem. It is shown that the speed of convergence is quite independent of step size even for very large time steps. This makes it possible to design strategies in which the mesh gets gradually refined during the iteration in such a way that the iteration error stays essentially on the level of discretization error.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4102400
zbMATH Keywords: waveform relaxation
zbMATH Keywords: weak coupling
zbMATH Keywords: mesh refinement
zbMATH Keywords: Picard-Lindelöf iteration
zbMATH Keywords: systems
zbMATH Keywords: speed of convergence
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01952687
OpenAlex ID: W2886312243
description: scientific article; zbMATH DE number 4102400