文章基本信息

标题：Numerical algorithms for the time-space tempered fractional Fokker-Planck equation
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作者：Xiaorui Sun ; Fengqun Zhao ; Shuiping Chen 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2017
卷号：2017
期号：1
页码：259
DOI：10.1186/s13662-017-1317-9
语种：English
出版社：Hindawi Publishing Corporation
摘要：This paper aims to provide the high order numerical schemes for the time-space tempered fractional Fokker-Planck equation in a finite domain. The high order difference operators, called the tempered and weighted and shifted Lubich difference operators, are used to approximate the time tempered fractional derivative. The spatial operators are discretized by the central difference methods. We apply the central difference methods to the spatial operators and obtain that the numerical schemes are convergent with orders O ( τ q + h 2 ) $O( au^{q} + h^,)$ ( q = 1 , 2 , 3 , 4 , 5 $q = 1,2,3,4,5$ ). The stability and convergence of the first order numerical scheme are rigorously analyzed. And the effectiveness of the presented schemes is testified with several numerical experiments. Additionally, some physical properties of this diffusion system are simulated.
关键词：tempered fractional Fokker-Planck equation ; weighted and shifted Lubich difference operators ; fractional central difference operator ; stability ; convergence