A New Numerical Method for the Riesz Space Fractional Diffusion Equation
Firstly, using matrix transform method, we transform the Riesz space fractional diffusion equation into an ordinary differential equation, and get its analytic solution. Secondly, we use (2,1) Pade approxiation to the exponentinal matrix of the analytic solution and obtain a new difference scheme for solving Riesz space fractional diffusion equation. Finally, we prove that the difference scheme is unconditionally stable.
H. F. Ding et al., "A New Numerical Method for the Riesz Space Fractional Diffusion Equation", Advanced Materials Research, Vol. 213, pp. 393-396, 2011