Finite difference approximation method for a space fractional convection-diffusion equation with variable coefficients

Abstract

Space non-integer order convection-diffusion descriptions are generalized form of integer order convection-diffusion problems expressing super diffusive and convective transport processes. In this article, we propose finite difference approximation for space fractional convection-diffusion model having space variable coefficients on the given bounded domain over time and space. It is shown that the Crank-Nicolson difference scheme based on the right shifted Grünwald-Letnikov difference formula is unconditionally stable and it is also of second order consistency both in temporal and spatial terms with extrapolation to the limit approach. Numerical experiments are tested to verify the efficiency of our theoretical analysis and confirm order of convergence.