  In this paper, a second-order backward difference formula (abbr. BDF2) is
used to approximate first-order time partial derivative, the Riesz fractional
derivatives are approximated by fourth-order compact operators, a class of new
alternating-direction implicit difference scheme (abbr. ADI) is constructed for
two-dimensional Riesz space fractional nonlinear reaction-diffusion equation.
Stability and convergence of the numerical method are analyzed. Numerical
experiments demonstrate that the proposed method is effective.
