Approximating Lyapunov exponents and Sacker-Sell spectrum for retarded functional differential equations. (English) Zbl 1284.65082
Summary: We consider Lyapunov exponents and the 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 reduction 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.
MSC:
| 65L03 | Numerical methods for functional-differential equations |
| 34K06 | Linear functional-differential equations |
| 34K08 | Spectral theory of functional-differential operators |
| 65L07 | Numerical investigation of stability of solutions to ordinary differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 37M25 | Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
Lyapunov exponents; Sacker-Sell spectrum; retarded functional differential equations; Hilbert space; discrete QR method; collocation; Fourier projection; error analysis; stability; numerical examplesSoftware:
dde23References:
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