Abstract
This chapter elaborates about the Monte Carlo method applicable to linear elliptic partial differential equations. A numerical approximation to the solution of a linear elliptic partial differential equation at a single point is obtained. Simulation of the motion of a random particle may be used to approximate the solution to linear elliptic equations. The steps for this method are straightforward. First, approximate the given elliptic partial differential equation by a finite difference method. Rewrite the finite difference formula as a recursive function for the value of the unknown at any given point. Then, interpret this recursive formula as a set of transition probabilities that determine the motion of a random particle.
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