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Zbl 1167.65419
Chen, S.; Liu, F.; Zhuang, P.; Anh, V.
Finite difference approximations for the fractional Fokker-Planck equation. (English)
[J] Appl. Math. Modelling 33, No. 1, 256-273 (2009). ISSN 0307-904X

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.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
26A33 Fractional derivatives and integrals (real functions)
35K55 Nonlinear parabolic equations

Keywords: fractional Fokker-Planck equation; finite difference approximation; stability; energy method

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Zentralblatt MATH Berlin [Germany]