  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.
