Abstract
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.
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