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题名: Numerical Algorithms for the Forward and Backward Fractional Feynman-Kac Equations
作者: Deng, WH(邓伟华); Chen, MH; Barkai, E
收录类别: SCIE ; EI
出版日期: 2015-03
刊名: JOURNAL OF SCIENTIFIC COMPUTING
卷号: 62, 期号:3, 页码:718-746
出版者: SPRINGER
出版地: NEW YORK
英文摘要: The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a Schrodinger equation in imaginary time. The functionals of non-Brownian motion, or anomalous diffusion, follow the fractional Feynman-Kac equation (Carmi et al. in J Stat Phys 141: 1071-1092, 2010), where the fractional substantial derivative is involved. Based on recently developed discretized schemes for fractional substantial derivatives (Chen and Deng arXiv:1310.3086), this paper focuses on providing algorithms for numerically solving the forward and backward fractional Feynman-Kac equations; since the fractional substantial derivative is non-local time-space coupled operator, new challenges are introduced compared with the ordinary fractional derivative. Two ways (finite difference and finite element) of discretizing the space derivative are considered. For the backward fractional Feynman-Kac equation, the numerical stability and convergence of the algorithms with first order accuracy are theoretically discussed; and the optimal estimates are obtained. For all the provided schemes, including the first order and high order ones, of both forward and backward Feynman-Kac equations, extensive numerical experiments are performed to show their effectiveness.
关键词: Fractional Feynman-Kac equation ; Fractional substantial derivative ; Optimal convergent order ; Numerical stability and convergence ; Numerical inversion of Laplace transforms
作者部门: [Deng, Weihua ; Chen, Minghua] Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Peoples R China ; [Barkai, Eli] Bar Ilan Univ, Dept Phys, Adv Mat & Nanotechnol Inst, IL-52900 Ramat Gan, Israel
通讯作者: Deng, WH (reprint author), Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Peoples R China.
学科分类: Mathematics
文章类型: Article
所属项目编号: National Natural Science Foundation of China [11271173] ; Fundamental Research Funds for the Central Universities [lzujbky-2014-228]
所属项目名称: 国家自然科学基金项目 ; 中央高校基本科研业务费专项资金
项目资助者: NSFC ; LZU
语种: 英语
DOI: 10.1007/s10915-014-9873-6
ISSN号: 0885-7474
WOS记录号: WOS:000348984100005
EI记录号: 20143600013169
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内容类型: 期刊论文
URI标识: http://ir.lzu.edu.cn/handle/262010/118978
Appears in Collections:数学与统计学院_期刊论文

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Recommended Citation:
Deng, WH,Chen, MH,Barkai, E. Numerical Algorithms for the Forward and Backward Fractional Feynman-Kac Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2015,62(3):718-746.
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