International Journal of Differential Equations

Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

Qianqian Yang, Fawang Liu, and Ian Turner

Full-text: Open access

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 (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.

Article information

Source
Int. J. Differ. Equ., Volume 2010, Special Issue (2010), Article ID 464321, 22 pages.

Dates
Received: 25 May 2009
Revised: 20 August 2009
Accepted: 28 September 2009
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399866

Digital Object Identifier
doi:10.1155/2010/464321

Mathematical Reviews number (MathSciNet)
MR2575294

Zentralblatt MATH identifier
1203.82068

Citation

Yang, Qianqian; Liu, Fawang; Turner, Ian. Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term. Int. J. Differ. Equ. 2010, Special Issue (2010), Article ID 464321, 22 pages. doi:10.1155/2010/464321. https://projecteuclid.org/euclid.ijde/1485399866


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