Solution of the fractional diffusion equation with the Riesz fractional derivative using McCormack method

This paper aims to approximate the fractional diffusion equations with the Riesz fractional derivative in a finite domain utilizing the McCormack numerical method with a second order accuracy. To approximate the Riesz fractional derivative, the fractional central difference is used. The fractional derivative error is obtained for the central fractional difference and the stability of the McCormack numerical method is studied. Some numerical examples are given to evidence the maximum error obtained when the McCormack method is utilized for the solution of the fractional diffusion equations using the fractional central difference.