An integration scheme for reaction-diffusion models

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 is more convenient to be employed for systems with 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 us to treat systems with very complicated boundary conditions.