Stability radius of polynomials occurring in the numerical solution of initial value problems
type: Item
instance of: scholarly article
title: Stability radius of polynomials occurring in the numerical solution of initial value problems
zbMATH Open document ID: 0711.65067
DOI: 10.1007/BF01931665
author: Roeland P. van der Marel
published in: BIT
publication date: 1990-01-01T00:00:00Z
review text: Let \(T_{mp}\) be the set of all polynomials \(\phi\) (x) with real coefficients and degree \(\leq m\) for which \(\phi (x)=\exp (x)+O(x^{p+1})\) (for \(x\to 0)\) holds. \(\phi\) occurs in many numerical methods for initial value problems of ordinary differential equations and for initial-boundary value problems of partial differential equations. Motivated by stability requirements, denote by r(\(\phi\)) the radius of the largest disk \(D(\rho)=\{z\in C:| z+\rho | \leq \rho \}\) contained in the stability region \(S(\rho)=\{z\in C:| \phi (z)| \leq 1\}\). Then some conclusions are given which deal with \(r_{mp}=\sup \{r(\phi):\phi \in T_{mp}\}\).
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 4169999
zbMATH Keywords: stability radius of polynomials
zbMATH Keywords: circle condition
zbMATH Keywords: stability region
reviewed by: Miroslav Bartušek
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01931665
OpenAlex ID: W1967645362
description: scientific article; zbMATH DE number 4169999