An efficient spectral-Galerkin method for fractional reaction-diffusion equations in unbounded domains

In this work, we apply a fast and accurate numerical method for solving fractional reaction-diffusion equations in unbounded domains. By using the Fourier-like spectral approach in space, this method can effectively handle the fractional Laplace operator, leading to a fully diagonal representation of the fractional Laplacian. To fully discretize the underlying nonlinear reaction-diffusion systems, we propose to use an accurate time marching scheme based on ETDRK4. Numerical examples are presented to illustrate the effectiveness of the proposed method.