We consider Lyapunov exponents and Sacker–Sell spectrum for linear, nonautonomous retarded functional differential equations posed on an appropriate Hilbert space. A numerical method is proposed to approximate such quantities, based on the eduction to finite dimension of the evolution family associated to the system, to which a classic discrete QR method is then applied. The discretization of the evolution family is accomplished by a combination of collocation and generalized Fourier projection. A rigorous error analysis is developed to bound the difference between the computed stability spectra and the exact stability spectra. The efficacy of the results is illustrated with some numerical examples.
Approximating Lyapunov exponents and Sacker-Sell spectrum for retarded functional differential equations
BREDA, Dimitri;
2014-01-01
Abstract
We consider Lyapunov exponents and Sacker–Sell spectrum for linear, nonautonomous retarded functional differential equations posed on an appropriate Hilbert space. A numerical method is proposed to approximate such quantities, based on the eduction to finite dimension of the evolution family associated to the system, to which a classic discrete QR method is then applied. The discretization of the evolution family is accomplished by a combination of collocation and generalized Fourier projection. A rigorous error analysis is developed to bound the difference between the computed stability spectra and the exact stability spectra. The efficacy of the results is illustrated with some numerical examples.File | Dimensione | Formato | |
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