Numerical schemes of the time tempered fractional Feynman-Kac equation

被引：11
|
作者：
Deng, W. H. [1 ]
Zhang, Z. J. [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & Complex Syst, Lanzhou 730000, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Tempered fractional substantial derivative; Feynman-Kac equation; Finite difference approximation; Finite element approximation; FINITE-DIFFERENCE APPROXIMATIONS; DIFFUSION; ALGORITHMS; DISPERSION; RESIDENCE;
D O I：
10.1016/j.camwa.2016.12.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper focuses on providing the computation methods for the backward time tempered fractional Feynman-Kac equation, being one of the models recently proposed in Wu et al. (2016). The discretization for the tempered fractional substantial derivative is derived, and the corresponding finite difference and finite element schemes are designed with well established stability and convergence. The performed numerical experiments show the effectiveness of the presented schemes. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1063 / 1076
页数：14
相关论文
共 50 条
  • [1] TIME DISCRETIZATION OF A TEMPERED FRACTIONAL FEYNMAN-KAC EQUATION WITH MEASURE DATA
    Deng, Weihua
    Li, Buyang
    Qian, Zhi
    Wang, Hong
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (06) : 3249 - 3275
  • [2] Tempered fractional Feynman-Kac equation: Theory and examples
    Wu, Xiaochao
    Deng, Weihua
    Barkai, Eli
    [J]. PHYSICAL REVIEW E, 2016, 93 (03)
  • [3] High Order Algorithm for the Time-Tempered Fractional Feynman-Kac Equation
    Chen, Minghua
    Deng, Weihua
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2018, 76 (02) : 867 - 887
  • [4] Numerical methods for forward fractional Feynman-Kac equation
    Nie, Daxin
    Sun, Jing
    Deng, Weihua
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2024, 50 (03)
  • [5] Compact finite difference schemes for the backward fractional Feynman-Kac equation with fractional substantial derivative
    Hu, Jiahui
    Wang, Jungang
    Nie, Yufeng
    Luo, Yanwei
    [J]. CHINESE PHYSICS B, 2019, 28 (10)
  • [6] Fractional Feynman-Kac equation for weak ergodicity breaking
    Carmi, Shai
    Barkai, Eli
    [J]. PHYSICAL REVIEW E, 2011, 84 (06)
  • [7] Two L1 Schemes on Graded Meshes for Fractional Feynman-Kac Equation
    Chen, Minghua
    Jiang, Suzhen
    Bu, Weiping
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2021, 88 (03)
  • [8] Two L1 Schemes on Graded Meshes for Fractional Feynman-Kac Equation
    Minghua Chen
    Suzhen Jiang
    Weiping Bu
    [J]. Journal of Scientific Computing, 2021, 88
  • [9] Feynman-Kac equation revisited
    Wang, Xudong
    Chen, Yao
    Deng, Weihua
    [J]. PHYSICAL REVIEW E, 2018, 98 (05)
  • [10] High Order Algorithm for the Time-Tempered Fractional Feynman–Kac Equation
    Minghua Chen
    Weihua Deng
    [J]. Journal of Scientific Computing, 2018, 76 : 867 - 887
12345