Semigroup discretization and spectral approximation for linear nonautonomous delay differential equations

Autor:	Breda, Dimitri, Maset, Stefano, Vermiglio, Rossana
Rok vydání:	2010
Předmět:	Mathematics - Numerical Analysis 34K30 34L16 65L03 65L07 65L15 47D06
Druh dokumentu:	Working Paper
Popis:	This paper deals with the approximation of the spectrum of linear and nonautonomous delay differential equations through the reduction of the relevant evolution semigroup from infinite to finite dimension. The focus is placed on classic collocation, even though the requirements that a numerical scheme has to fulfill in order to allow for a correct approximation of the spectral elements are recalled. This choice, motivated by the analyticity of the underlying eigenfunctions, allows for a convergence of infinite order, as rigorously demonstrated through a priori error bounds when Chebyshev nodes are adopted. Fundamental applications such as determination of asymptotic stability of equilibria (autonomous case) and limit cycles (periodic case) follow at once. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1001.4657 Zobrazit plný text záznamu View this record from Arxiv