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We study a second order scheme for spatial fractional differential equationswith variable coefficients. Previous results mainly concentrate on equationswith diffusion coefficients that are proportional to each other. In this paper,by further study on the generating function of the discretization matrix,second order convergence of the scheme is proved for diffusion coefficientssatisfying a certain condition but are not necessary to be proportional. Thetheoretical results are justified by numerical tests.

On a second order scheme for space fractional diffusion equations with variable coefficients