A high order compact finite difference scheme for time fractional Fokker–Planck equations

In this paper, a high order compact (HOC) scheme for time fractional Fokker–Planck equations with variable convection is constructed. The scheme is studied using its matrix form by the energy method. We find that the difficulty arising from the variable coefficient can be overcome by simple modifications of the coefficient matrices. The scheme is shown to be stable and convergent with order τ2−α+h4τ2−α+h4 which is higher than some recently studied schemes. Numerical examples are given to justify the theoretical analysis.