Title :
The finite element method for the generalized space fractional Fokker-Planck equation
Author :
Zhao, Zhengang ; Li, Changpin
Author_Institution :
Dept. of Math., Shanghai Univ., Shanghai, China
Abstract :
In this paper, we derive the finite element method for the numerical solution of the Generalized space fractional order (fractional for simplicity) Fokker-Planck equation, which the space fractional derivatives are the left and right Riemann-Liouville derivatives that can be used to describe Lévy flights. The fully discrete numerical approximation is analyzed, where the Galerkin finite element method for the space Riemann-Liouville fractional derivatives with order 1 + β ∈ [1, 2) and γ ∈ (0, 1]. Results on variational solution of the error estimates are presented. Numerical examples are included to confirm the theoretical estimates.
Keywords :
Fokker-Planck equation; Galerkin method; finite element analysis; partial differential equations; random processes; transport processes; Galerkin finite element method; Levy flights; generalized space fractional Fokker-Planck equation; left Riemann-Liouville derivatives; numerical solution; right Riemann-Liouville derivatives; space fractional derivatives; Polynomials; Lévy flights; Riemann-Liouville derivative; Space fractional Fokker-Planck equation; finite element method;
Conference_Titel :
Mechatronics and Embedded Systems and Applications (MESA), 2010 IEEE/ASME International Conference on
Conference_Location :
Qingdao, ShanDong
Print_ISBN :
978-1-4244-7101-0
DOI :
10.1109/MESA.2010.5552008
