Spectral discretization of a class of linear integro-differential model equations

In this paper a class of simple model equations is used in order to shed light on some features of the dynamics of the travelling waves that are solutions of evolutionary convection-diffusion models subject to a ``global'' reaction term. The analysis here performed for the associated eigenvalue problem is based on a spectral collocation technique and on Chebyshev polynomials. The discretization of both derivative and integral terms are carried out by taking advantage of recent software libraries and by a suitable implementation of various boundary conditions. The obtained numerical results are compared with some analytical results available for simple cases and the same spectral discretization is employed in order to investigate the non normality degree of the operator by means of its pseudospectrum.