A Hermite Spectral Method For Fractional Convection Diffusion Equations On Unbounded Domains

In this paper, a Hermite spectral method is used for solving the fractional convection diffusion equations on unbounded domains. The scaled Hermite functions are used as basis functions, and the problems are solved in Fourier space. Multi-dimensional problems are considered in this paper, and the errors are estimated in Fourier space as well. At the end of the paper, the method is introduced to solve the fractional convection diffusion equations. Numerical examples are presented to verify our results.