Solving partial differential equations via random walks: A review

Abstract

In the probabilistic potential theory, it has been well known that there is a one-to-one correspondence between a partial differential operator and a series of random walks. Based on this, one can solve a large class of elliptic partial differential equations such as Laplace, Poisson, linearized Poisson-Boltzmann equations and so on by simulating the corresponding random walks. In this chapter, we review the theory, its algorithm implementations and some applications in scientific problems. © 2012 Nova Science Publishers, Inc. All rights reserved.