TIME DISCRETIZATION OF A TEMPERED FRACTIONAL FEYNMAN-KAC EQUATION WITH MEASURE DATA

被引：23

作者：

Deng, Weihua ^{[1
]}

Li, Buyang ^{[2
]}

Qian, Zhi ^{[3
]}

Wang, Hong ^{[4
]}

机构：

[1] Lanzhou Univ, Gansu Key Lab Appl Math & Complex Syst, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong, Peoples R China

[3] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[4] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2018年 / 56卷 / 06期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

tempered fractional operators; Feynmann-Kac equation; integral representation; convolution quadrature; convergence; CONVOLUTION QUADRATURE; EVOLUTION EQUATION; NUMERICAL-SOLUTION; DIFFUSION; APPROXIMATIONS;

D O I：

10.1137/17M1118245

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A feasible approach to study tempered anomalous dynamics is to analyze its functional distribution, which is governed by the tempered fractional Feynman-Kac equation. The main challenges of numerically solving the equation come from the time-space coupled nonlocal operators and the complex parameters involved. In this work, we introduce an efficient time-stepping method to discretize the tempered fractional Feynman-Kac equation by using the Laplace transform representation of convolution quadrature. Rigorous error estimate for the discrete solutions is carried out in the measure norm. Numerical experiments are provided to support the theoretical results.

引用

页码：3249 / 3275

页数：27

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