Hybrid computer solutions of partial differential equations by Monte Carlo methods

Abstract

In addition to finite-difference methods, Monte Carlo methods also are known for solving certain partial differential equations. When implemented on a digital computer, however, the Monte Carlo methods have generally proven to be very inefficient. In 1960, a study carried out at the University of Michigan described analog computer techniques for mechanizing Monte Carlo methods. From the Michigan study it became evident that a fast analog computer together with a small digital computer and a modest interface could obtain Monte Carlo solutions at rates competitive with standard finite-difference methods.