The stability of rational approximations of cosine functions on Hilbert spaces
type: Item
instance of: scholarly article
title: The stability of rational approximations of cosine functions on Hilbert spaces
zbMATH Open document ID: 1160.65019
author: M. J. Moreta
author: I. Alonso-Mallo
author: Begoña Cano
published in: Applied Numerical Mathematics
publication date: 2008-12-16T00:00:00Z
review text: An abstract initial value problem of second order in time of the following type \[ u^{\prime \prime}(t) =-Au(t), \;\;t\in \mathbb R, \;\;\;u(0)=u_0, \;\;u^{\prime}(0)=v_0 \] with densely defined closed linear operator \(A\) on some complex Hilbert space is investigated. The operator is supposed to generate a cosine function (the problem is well posed). So called rational methods for the time discretization of this problem are considered. The presented results extended previous results obtained for selfadjoint operators. Stability for the proposed rational methods is proved under some hypotheses and in the particular case for Runge-Kutta and Runge-Kutta-Nyström methods the conditions where the hypotheses for stability are fulfilled are stated.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 5382927
zbMATH Keywords: second order in time evolutionary problems
zbMATH Keywords: Hilbert space
zbMATH Keywords: stability
zbMATH Keywords: rational methods
zbMATH Keywords: Runge-Kutta-Nyström methods
zbMATH Keywords: abstract initial value problem
MaRDI profile type: Publication
full work available at URL: j.apnum.2007.11.022
OpenAlex ID: W2065738136
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DOI: 10.1016/J.APNUM.2007.11.022
description: scientific article; zbMATH DE number 5382927