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

Abstract

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.

arXiv comment23 pages

References in corpus (8)

• A new difference scheme for the time fractional diffusion equation
• A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations
• Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach
• Fractional Reaction-Diffusion Equation
• On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation
• A short FE implementation for a 2d homogeneous Dirichlet problem of a Fractional Laplacian
• Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
• Phase portrait control for 1D monostable and bistable reaction-diffusion equations