The stability of an equilibrium point of a dynamical system is determinedby the position in the complex plane of the so-called characteristic values of the linearizationaround the equilibrium. This paper presents an approach for the computationof characteristic values of partial differential equations of evolution involving timedelay, which is based on a pseudospectral method coupled with a spectral method.The convergence of the computed characteristic values is of infinite order with respectto the pseudospectral discretization and of finite order with respect to the spectralone. However, for one dimensional reaction diffusion equations, the finite order of thespectral discretization is proved to be so high that the convergence turns out to be asfast as one of infinite order.
