  A detailed description and validation of a recently developed integration
scheme is here reported for one- and two-dimensional reaction-diffusion models.
As paradigmatic examples of this class of partial differential equations the
complex Ginzburg-Landau and the Fitzhugh-Nagumo equations have been analyzed.
The novel algorithm has precision and stability comparable to those of
pseudo-spectral codes, but it is more convenient to employ for systems with
quite large linear extention $L$. As for finite-difference methods, the
implementation of the present scheme requires only information about the local
enviroment and this allows to treat also system with very complicated boundary
conditions.
