A numerical approach to the generalized nonlinear fractional Fokker-Planck equation

Authors:
Zhengang Zhao;Changpin Li
Affiliations:
Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, China;Department of Mathematics, Shanghai University, Shanghai 200444, China
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

In this paper, we propose a fully discrete Galerkin finite element method to solve the generalized nonlinear fractional Fokker-Planck equation, which has a multi-fractional-spatial-operator characteristic that describes the Levy flight. In the time direction, we use the finite difference method, and in the spatial direction we use the fractional finite element method in the framework of the fractional Sobolev spaces. We derive a fully discrete scheme for the considered equation. We prove the existence and uniqueness of the discrete solution and give the error estimates. The numerical examples are also included which support the theoretical analysis.