An integration scheme for reaction-diffusion models

TL;DR

This paper presents a new integration scheme for reaction-diffusion models that offers high precision and stability, is computationally convenient for large systems, and handles complex boundary conditions effectively.

Contribution

The paper introduces a novel integration algorithm for reaction-diffusion PDEs that combines spectral accuracy with local computation advantages, suitable for large and complex systems.

Findings

Comparable precision and stability to pseudo-spectral methods

More convenient for large systems with extensive spatial domains

Handles complex boundary conditions efficiently

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 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.