Lyapunov exponents of renewal equations: Numerical approximation and convergence analysis

We propose a numerical method for computing the Lyapunov exponents of renewal equations (delay equations of Volterra type), consisting first of applying a discrete QR technique to the associated evolution family suitably posed on a Hilbert state space, and second in reducing to a finite dimension each evolution operator in the obtained time sequence. The reduction to finite dimension relies on a 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.