  A one dimensional fractional diffusion model with the Riemann-Liouville
fractional derivative is studied. First, a second order discretization for this
derivative is presented and then an unconditionally stable weighted average
finite difference method is derived. The stability of this scheme is
established by von Neumann analysis. Some numerical results are shown, which
demonstrate the efficiency and convergence of the method. Additionally, some
physical properties of this fractional diffusion system are simulated, which
further confirm the effectiveness of our method.
