Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term
Joint Authors
Liu, Fawang
Turner, I. W.
Yang, Qianqian
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-01-05
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
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 (TSFFPENST), 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 Grünwald 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.
American Psychological Association (APA)
Yang, Qianqian& Liu, Fawang& Turner, I. W.. 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،Vol. 2010, no. 2010, pp.1-22.
https://search.emarefa.net/detail/BIM-473641
Modern Language Association (MLA)
Yang, Qianqian…[et al.]. 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 No. 2010 (2010), pp.1-22.
https://search.emarefa.net/detail/BIM-473641
American Medical Association (AMA)
Yang, Qianqian& Liu, Fawang& Turner, I. W.. 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. Vol. 2010, no. 2010, pp.1-22.
https://search.emarefa.net/detail/BIM-473641
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473641