The mean exit time and transition probability density function are macroscopic quantities used to determine the behavior of stochastic di... Show moreThe mean exit time and transition probability density function are macroscopic quantities used to determine the behavior of stochastic di↵erential equations (SDEs). The integral-di↵erential equations determining these quantities for SDEs with non- Gaussian ↵-stable L´evy motions involve a nonlocal term consisting of a singular integral, which is a manifestation of the ’flights’ or ’jumps’ due to the non-Gaussian noise. A two-dimensional SDE with radially symmetric ↵-stable L´evy motion is considered, and an efficient second-order accurate numerical scheme is developed for calculating the mean exit time and transition probability density function. The scheme is numerically verified by testing the results of the deterministic integral-di↵erential equations with a known, smooth function u(x) in place of themean exit time, and by calculating an unknown mean exit time u(x). M.S. in Applied Mathematics, May 2016 Show less