A numerical method for solving the time fractional reaction-diffusion equation with variable coefficients on the whole line

Abstract

This paper focuses on numerically solving the time fractional reaction-diffusion equation on the whole line. A numerical scheme is constructed based on Hermite pseudospectral method, we use finite difference scheme in time direction while Hermite-Gauss points in space. Several numerical results for the Hermite pseudospectral scheme are provided to confirm that a second-order time accuracy and spectral accuracy in space can be obtained.