Generalized Hermite Spectral Method for Nonlinear Fokker-Planck Equations on the Whole Line

Abstract

In this paper, we develop a spectral method for the nonlinear Fokker-Planck equations modeling the relaxation of fermion and boson gases. A full-discrete generalized Hermite spectral scheme is constructed. Its convergence and stability are proved strictly. Numerical results show the efficiency of this approach and coincide well with theoretical analysis.