Finite difference approximations for the fractional Fokker-Planck equation. (English) Zbl 1167.65419

Summary: 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.


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
35K55 Nonlinear parabolic equations
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