A fixed random walk Monte Carlo computation of potential inside two Conducting oblate spheroidal shells

This paper presents a fixed random walk Monte Carlo method for computing potential distribution within two conducting oblate spheroidal shells at different potential. An explicit finite difference method for solving Laplace's equation in oblate spheroidal coordinates systems for an axially symmetric geometry has been developed. This was used to determine the transition probabilities for the fixed random walk Monte Carlo method used. An ingenious strategy was created to overcome the singularity problems encountered in the oblate spheroid pole regions. The potential computation results obtained did fall in the same range with those obtained using finite difference method and exact solution.