  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.
