Finite difference approximations for the fractional Fokker–Planck equation☆

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Abstract

The fractional Fokker–Planck equation has been used in many physical transport problems which take place under the influence of an external force field. In this paper we examine some practical numerical methods to solve a class of initial-boundary value problems for the fractional Fokker–Planck equation on a finite domain. The solvability, stability, consistency, and convergence of these methods are discussed. Their stability is proved by the energy method. Two numerical examples are also presented to evaluate these finite difference methods against the exact analytical solutions.

Keywords

Fractional Fokker–Planck equation
Finite difference approximation
Stability
The energy method

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This research has been supported by the Australian Research Council Grant No LP0348653 and the National Natural Science Foundation of China Grant No 10271098. The authors thank the referees for their thoughtful suggestions.

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