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

TL;DR

This paper introduces a spectral-Galerkin numerical method combining Fourier-like spectral techniques and ETDRK4 time-stepping to efficiently solve fractional reaction-diffusion equations in unbounded domains, demonstrating high accuracy and effectiveness.

Contribution

The paper presents a novel spectral-Galerkin approach with a diagonal fractional Laplacian representation and an ETDRK4 scheme for nonlinear systems, improving computational efficiency and accuracy.

Findings

Method effectively handles fractional Laplacian in unbounded domains

Numerical examples confirm high accuracy and efficiency

Approach suitable for complex fractional reaction-diffusion problems

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.