Approximation of eigenvalues of evolution operators for linear retarded functional differential equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.34089
DOI: 10.1137/100815505
author: S. Maset
author: D. Breda
author: R. Vermiglio
published in: SIAM Journal on Numerical Analysis
publication date: 2012-08-23T00:00:00Z
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34L16
Mathematics Subject Classification ID: 65L03
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34K08
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 6070626
zbMATH Keywords: retarded functional differential equations
zbMATH Keywords: eigenvalue approximations
zbMATH Keywords: evolution operators
zbMATH Keywords: pseudospectral collocation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1137/100815505
OpenAlex ID: W2032206170
title: Approximation of eigenvalues of evolution operators for linear retarded functional differential equations
review text: The authors consider for the linear retarded functional differential equation NEWLINE\[NEWLINEy'(t)=f(t,y_t), \, t\in INEWLINE\]NEWLINE the reduction to finite dimension of the relevant evolution operators by a pseudospectral collocation and study how the nonzero eigenvalues of such operators are approximated by the eigenvalues of their finite-dimensional versions. The most relevant applications such as the determination of the asymptotic stability of equilibria and periodic solutions of nonlinear autonomous retarded functional differential equations are also discussed. Numerical tests are provided.
reviewed by: Sotiris K. Ntouyas
description: scientific article; zbMATH DE number 6070626