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

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