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| Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of non-locality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. Here, we will introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains. We will also provide a biophysical interpretation for the fractional Laplacian in problems related to excitable media, with broad applications in cardiac electrophysiology. |
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