Abstract
A numerical method for a kind of time-dependent two-dimensional two-sided space fractional diffusion equations is developed in this paper. The proposed method combines a time scheme based on direction splitting approaches and a spectral method for the spatial discretization. The direction splitting approach renders the underlying two-dimensional equation into a set of one-dimensional space fractional diffusion equations at each time step. Then these one-dimensional equations are solved by using the spectral method based on weak formulations. A time error estimate is derived for the semi-discrete solution, and the unconditional stability of the fully discretized scheme is proved. Some numerical examples are presented to validate the proposed method.
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