A Fourth-Order Compact ADI Scheme for Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation

Abstract: 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.