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Title: Time discretization of a tempered fractional Feynman-Kac equation with measure data
Authors: Deng, W
Li, B 
Qian, Z
Wang, H
Issue Date: 2018
Source: SIAM journal on numerical analysis, 2018, v. 56, no. 6, p. 3249-3275
Abstract: 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.
Keywords: Convergence
Convolution quadrature
Feynmann-Kac equation
Integral representation
Tempered fractional operators
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on numerical analysis 
ISSN: 0036-1429
EISSN: 1095-7170
DOI: 10.1137/17M1118245
Rights: © 2018, Society for Industrial and Applied Mathematics.
Posted with permission of the publisher.
The following publication Deng, W., Li, B., Qian, Z., & Wang, H. (2018). Time discretization of a tempered fractional Feynman--Kac equation with measure data. SIAM Journal on Numerical Analysis, 56(6), 3249-3275 is available at https://dx.doi.org/10.1137/17M1118245
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