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

International Journal of Differential Equations, 2010, vol. 2010, 1-22

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 ð ›¼ ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order 𠜇 ∈ (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.

Date: 2010
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJDE/2010/464321.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJDE/2010/464321.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:464321

DOI: 10.1155/2010/464321

Access Statistics for this article

More articles in International Journal of Differential Equations from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().