Numerical Approximations for the Fractional Fokker-Planck Equation with Two-Scale Diffusion

Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing numerical discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we first derive the fractional Fokker-Planck equation with two-scale diffusion from the Levy process framework, and then the fully discrete scheme is built by using the L-1 scheme for time discretization and finite element method for space. With the help of the sharp regularity estimate of the solution, we optimally get the spatial and temporal error estimates. Finally, we validate the effectiveness of the provided algorithm by extensive numerical experiments.

Automated summary

In this paper, the fractional Fokker-Planck equation with two-scale diffusion is derived from the Levy process framework. A fully discrete scheme is then built using the L-1 scheme for time discretization and finite element method for space. The effectiveness of the algorithm is validated through extensive numerical experiments.