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

fYear

2010

Firstpage

511

Lastpage

516

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;

fLanguage

English

Publisher

ieee

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

Type

conf

DOI

10.1109/MESA.2010.5552008

Filename

5552008