Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Diffusion Equation

Abstract

In this paper, we develop a novel finite-difference scheme for the time-Caputo and space-Riesz fractional diffusion equation with convergence order $\mathcal {O}(\tau ^{2-\alpha } + h^2)$. The stability and convergence of the scheme are analyzed by mathematical induction. Moreover, some numerical results are provided to verify the effectiveness of the developed difference scheme.