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Mathematics > Numerical Analysis

arXiv:2404.11191 (math)
[Submitted on 17 Apr 2024]

Title:Lyapunov exponents of renewal equations: numerical approximation and convergence analysis

Authors:Dimitri Breda, Davide Liessi
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Abstract:We propose a numerical method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type), consisting first in applying a discrete QR technique to the associated evolution family suitably posed on a Hilbert state space and second in reducing to finite dimension each evolution operator in the obtained time sequence. The reduction to finite dimension relies on Fourier projection in the state space and on pseudospectral collocation in the forward time step. A rigorous proof of convergence of both the discretized operators and the approximated exponents is provided. A MATLAB implementation is also included for completeness.
Subjects: Numerical Analysis (math.NA); Dynamical Systems (math.DS)
Cite as: arXiv:2404.11191 [math.NA]
  (or arXiv:2404.11191v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2404.11191

Submission history

From: Davide Liessi [view email]
[v1] Wed, 17 Apr 2024 09:14:18 UTC (169 KB)
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