ABSTRACT
Unlike the deterministic numerical methods such as finite difference, finite elements, and moment methods, the floating random walk method is a nondeterministic (probabilistic or stochastic) numerical method employed in solving mathematical and physical problems. This chapter applies the floating random walk method to solve Laplace's and Poisson's equations for problems involving rectangular and axisymmetric solution regions that may or may not be inhomogeneous. As expected, the floating random walk method obtains an accurate solution in less time than the fixed random walk method. The computing procedure for solving an axisymmetric problem is summarized. The chapter illustrates the application of the floating random walk method by means of two numerical examples that have analytic solutions so that the accuracy and validity of the floating random walk method can be checked. The first example is an axisymmetric problem that involves a homogeneous solution region, whereas the second example involves an inhomogeneous solution region.
