Numerical schemes of the time tempered fractional Feynman-Kac equation

Abstract

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, Deng, and Barkai, Phys. Rev. E, 84 (2016) 032151]. 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.

21 pages, 2 figures

References in corpus (2)

• On distributions of functionals of anomalous diffusion paths
• Tempered Fractional Feynman-Kac Equation

Cited by in corpus (5)

• A Riesz basis Galerkin method for the tempered fractional Laplacian
• Error estimates for backward fractional Feynman-Kac equation with non-smooth initial data
• Galerkin finite element approximation for semilinear stochastic time-tempered fractional wave equations with multiplicative white noise and fractional Gaussian noise
• Numerical algorithms of the two-dimensional Feynman-Kac equation for reaction and diffusion processes
• High order algorithm for the time-tempered fractional Feynman-Kac equation