Feasibility study of Monte Carlo modelling techniques for distributed-parameter systems. Part 1: Discrete Monte Carlo models and their uses

Abstract

The theory of Monte Carlo modelling of distributed-parameter systems is developed from a difference-equation representation of the relevant partial differential equations. The analogy between this approach and that based on Kolmogorov's equation is used to simplify the resulting statistical model, and a number of extensions are proposed to deal with a variety of boundary types, nonlinearities, and forcing functions. The paper is completed by a series of examples illustrating the application of the extension using both digital and hybrid computers. A section is devoted to a critical assessment of the work described.