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Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Yang, Qianqian, Liu, Fawang, & Turner, Ian (2010) Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term. International Journal of Differential Equations, 2010, pp. 1-22.

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Abstract

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

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6 citations in Scopus
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ID Code: 37943
Item Type: Journal Article
Keywords: fractional Fokker-Planck equation, fractional derivative, numerical method, nonlinear source term, stability, convergence
DOI: 10.1155/2010/464321
ISSN: 1687-9643
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright © 2010 Qianqian Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Deposited On: 14 Oct 2010 11:34
Last Modified: 01 Mar 2012 00:23

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