ABSTRACT
Monte Carlo Methods (MCMs) have been applied successfully for solving differential and integral equations, finding eigenvalues, inverting matrices, and evaluating multiple integrals. MCMs are well known for solving static problems such as Laplace's or Poisson's equations. They are hardly applied in solving parabolic and hyperbolic partial differential equations. This chapter extends the applicability of the conventional MCM to the solution of time-dependent (heat) problems such as the heat equation in both rectangular and cylindrical coordinates. It deals with cases of rectangular solution regions as well as axisymmetric solution regions. The chapter presents results in one dimension (1-D) and two dimensions (2-D) that agree with the finite difference (FD) and exact solutions. The method does not require solving large matrices and is trivially easy to program. The idea can be extended to other time-dependent problems such as the wave equation.
