广义空间分数阶Fokker-Planck方程的有限元方法

Proceedings of 2010 IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications Pub Date : 2010-07-15 DOI:10.1109/MESA.2010.5552008

Zhengang Zhao, Changpin Li

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引用次数: 1

摘要

本文导出了广义空间分数阶(简称分数阶)Fokker-Planck方程数值解的有限元方法，该方程的空间分数阶导数是可用于描述l vy飞行的左、右Riemann-Liouville导数。分析了空间Riemann-Liouville分数阶导数(1 + β∈[1,2)，γ∈(0,1))的Galerkin有限元法的全离散数值逼近。给出了误差估计的变分解的结果。数值算例验证了理论估计。

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The finite element method for the generalized space fractional Fokker-Planck equation

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.

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Proceedings of 2010 IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications

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