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The discrete Monte Carlo method for the solution of partial differential equations has been studied theoretically and experimentally. A special purpose digital computer, the PDE machine, was designed and constructed from macromodules, and Monte Carlo solutions for illustrative problems were obtained. Error analysis has been made and experimental outcomes were compared with theoretical results. Using Monte Carlo methods the PDE machine has been proved to be very efficient from the viewpoint of accuracy and speed in comparison to the general purpose digital computer. Speeds of one solution every 2 seconds were obtained for Poisson's equations with a typical accuracy of better than 2 percent of the range of solutions.