Efficient numerical methods for the nonlinear two-sided space-fractional diffusion equation with variable coefficients

In this paper, a second order accurate time and space difference method is proposed to solve the nonlinear two-sided space-fractional diffusion equation with variable coefficients. We combine the alternating direction implicit method and Bi-conjugate gradient stabilized iterative solver to develop an efficient numerical method for a two dimensional, nonlinear, two-sided space-fractional diffusion equation with variable coefficients. Furthermore, the proposed method is proved to be uniquely solvable, stable and convergent. Finally, some numerical results verify the accuracy and efficiency of our computational approach.