  We use the mean exit time to quantify macroscopic dynamical behaviors of
stochastic dynamical systems driven by tempered L\'evy fluctuations, which are
solutions of nonlocal elliptic equations. Firstly, we construct a new numerical
scheme to compute and solve the mean exit time associated with the one
dimensional stochastic system. Secondly, we extend the analytical and numerical
results to two dimensional case: horizontal-vertical and isotropic case.
Finally, we verify the effectiveness of the presented schemes with numerical
experiments in several examples.
