Stability analysis of numerical methods for delay differential equations
type: Item
instance of: scholarly article
title: Stability analysis of numerical methods for delay differential equations
zbMATH Open document ID: 0724.65084
DOI: 10.1007/BF01385811
author: Karel J. in 't Hout
author: Marc N. Spijker
published in: Numerische Mathematik
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133580
review text: This paper deals with the stability analysis of step-by-step methods for the numerical solution of delay differential equations. We focus on the behaviour of such methods when they are applied to the linear test problem \(U'(t)=\lambda U(t)+\mu U(t-\tau)\) with \(\tau >0\) and \(\lambda\), \(\mu\) complex. A general theorem is presented which can be used to obtain complete characterizations of the stability regions of these methods.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 4195086
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: Schur polynomial
zbMATH Keywords: delay differential equations
zbMATH Keywords: stability regions
MaRDI profile type: Publication
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OpenAlex ID: W2082296130
description: scientific article; zbMATH DE number 4195086