A New Numerical Method for the Riesz Space Fractional Diffusion Equation

摘要

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.