A High Order Finite Difference/Spectral Approximations to the Time Fractional Diffusion Equations

Abstract

In this paper, we consider the numerical solution of a time-fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order α, with 03-α+N-m) , where Δt,N and m are the time step size, the polynomial degree and the regularity of the exact solution, respectively.