AN INTEGRATION SCHEME FOR REACTION–DIFFUSION MODELS

Massimo Nitti (), Alessandro Torcini () and Stefano Ruffo ()
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Massimo Nitti: Dipartimento di Sistemi e Informatica, via S. Marta 3, I-50139 Firenze, Italy
Alessandro Torcini: INFM, Udr Firenze, L. go E. Fermi 5, I-50125 Firenze, Italy;
Stefano Ruffo: Dipartimento di Energetica, via S. Marta 3, I-50139 Firenze, Italy, INFM and INFN, Italy

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 06, 1039-1050

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 extentionL. 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.

Keywords: Partial differential equations; Reaction–Diffusion models; Integration schemes (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000838

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