Abstract: Most studies of convection-diffusion equation are in the range of constant coefficient or integer order. To more accurately describe the solute movement features, the traditional integer order convection-diffusion equation is extended to cases of fractional order variable coefficient. The paper primarily investigated the finite difference decomposition method of Caputo fractional order convection-diffusion equation with variable coefficients. This paper introduced a half integer point, performed dual partitioning on the spatial grid,and then discretized the spatial derivatives using the finite difference method. Theoretical analysis shows that the solution of the discrete format proposed in this paper exists and is unique, with a convergence accuracy of ο(τ+h).The accuracy of theoretical analysis is verified using one-dimensional numerical examples.

Key words: fractional order, convection-diffusion equation, finite difference method, stability, convergence