Numerical schemes of the time tempered fractional Feynman-Kac equation

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.