The stability of an equilibrium point of a dynamical system is determined by the position in the complex plane of the so-called characteristic values of the linearization around the equilibrium. This work presents an approach for the computation of characteristic values of partial differential equations of evolution involving time delay, based on a coupled pseudospectral-spectral method. Convergence of computed values is of infinite order with respect to the pseudospectral discretization and of finite order with respect to the spectral one.
