  Space fractional convection diffusion equation describes physical phenomena
where particles or energy (or other physical quantities) are transferred inside
a physical system due to two processes: convection and superdiffusion. In this
paper, we discuss the practical alternating directions implicit method to solve
the two-dimensional two-sided space fractional convection diffusion equation on
a finite domain. We theoretically prove and numerically verify that the
presented finite difference scheme is unconditionally von Neumann stable and
second order convergent in both space and time directions.
