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Finite difference approximations for the fractional Fokker–Planck equation

Chen, S. , Liu, Fawang, Zhuang, Pinghui , & Anh, Vo V. (2008) Finite difference approximations for the fractional Fokker–Planck equation. Applied Mathematical Modelling, In Press.

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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.

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45 citations in Scopus
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42 citations in Web of Science®

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244 since deposited on 12 Sep 2008
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ID Code: 14804
Item Type: Journal Article
Keywords: Fractional Fokker–Planck equation, Finite difference approximation, Stability, The energy method
DOI: 10.1016/j.apm.2007.11.005
ISSN: 0307-904X
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Calculus of Variations Systems Theory and Control Theory (010203)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2008 Elsevier
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 12 Sep 2008
Last Modified: 29 Feb 2012 23:37

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