  This paper is concerned with the approximation of linear and
nonlinearinitial-boundary-value problems of pseudo-parabolic equations with
Dirichlet boundary conditions. They are discretized in space by spectral
Galerkin and collocation methods based on Legendre and Chebyshev polynomials.
The time integration is carried out suitably with robust schemes attending to
qualitative features such as stiffness and preservation of strong stability to
simulate nonregular problems more correctly. The corresponding semidiscrete and
fully discrete schemes are described and the performance of the methods is
analyzed computationally.
