Abstract
A numerical study of three problems is carried out using the gradient random walk method. These problems include the heat equation, Fitzhugh-Nagumo equation, and Burgers' equation. Each problem illustrates various aspects of the operation of the numerical method. The heat equation with no reaction term illustrates the numerical algorithm, the Fitzhugh-Nagumo equation is a system with an explicit reaction term, Burgers' equation has an advection term. The gradient random walk numerical method is well suited for the diffusion problem due to the connection between Gaussian distributions and the kernel of the heat equation. The numerical results compare well with known analytical solutions. Burgers' equation is studied to examine any effects the advection term has on the results of the numerical method.
Lindstrom, Gregory Scot (1993). Random walk computations of diffusive fields. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1993 -THESIS -L7533.