Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation

Abstract

A numerical method for the modified time fractional Fokker-Planck equation is proposed. Stability and convergence of the method are rigorously discussed by means of the Fourier method. We prove that the difference scheme is unconditionally stable, and convergence order is $O(\tau +h^{\mathrm{4}})$, where $\tau$ and $h$ are the temporal and spatial step sizes, respectively. Finally, numerical results are given to confirm the theoretical analysis.