Semigroup discretization and spectral approximation for linear nonautonomous delay differential equations

2010/01/26 by Dimitri Breda, Breda, Dimitri, Stefano Maset +3
Computer Science · Mathematics · #34K30 #34L16 #47D06 #65L03 #65L07 #65L15 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1001.4657

openalex publication_date 2010/01/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL

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