Semigroup discretization and spectral approximation for linear nonautonomous delay differential equations

摘要

This paper deals with the approximation of the spectrum of linear andnonautonomous delay differential equations through the reduction of therelevant evolution semigroup from infinite to finite dimension. The focus isplaced on classic collocation, even though the requirements that a numericalscheme has to fulfill in order to allow for a correct approximation of thespectral elements are recalled. This choice, motivated by the analyticity ofthe underlying eigenfunctions, allows for a convergence of infinite order, asrigorously demonstrated through a priori error bounds when Chebyshev nodes areadopted. Fundamental applications such as determination of asymptotic stabilityof equilibria (autonomous case) and limit cycles (periodic case) follow atonce.