Mixed generalized Hermite-Fourier spectral method for Fokker-Planck equation of periodic field

In this paper, we develop a mixed Hermite-Fourier spectral method for the Fokker-Planck equation of periodic field. Radical to the numerical solutions of partial differential equations of the sort, results on mixed generalized Hermite-Fourier orthogonal approximation are established. The convergence of the constructed spectral scheme is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis.