  In this paper, we present numerical methods to implement the probabilistic
representation of third kind (Robin) boundary problem for the Laplace
equations. The solution is based on a Feynman-Kac formula for the Robin problem
which employs the standard reflecting Brownian motion (SRBM) and its boundary
local time arising from the Skorohod problem. By simulating SRBM paths through
Brownian motion using Walk on Spheres (WOS) method, approximation of the
boundary local time is obtained and the Feynman-Kac formula is calculated by
evaluating the average of all path integrals over the boundary under a measure
defined through the local time. Numerical results demonstrate the accuracy and
efficiency of the proposed method for finding a local solution of the Laplace
equations with Robin boundary conditions.
