Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term
Data(s) |
2010
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Resumo |
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. |
Formato |
application/pdf |
Identificador | |
Publicador |
Hindawi Publishing Corporation |
Relação |
http://eprints.qut.edu.au/37943/1/37943P.pdf DOI:10.1155/2010/464321 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. |
Direitos |
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. |
Fonte |
Faculty of Science and Technology; Mathematical Sciences |
Palavras-Chave | #010302 Numerical Solution of Differential and Integral Equations #fractional Fokker-Planck equation #fractional derivative #numerical method #nonlinear source term #stability #convergence |
Tipo |
Journal Article |