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A stochastic method for the solution of the diffusion equation

Manuel Païva Institut de Recherche Interdisciplinaire en Biologie Humaine et Nucléaire (Groupe Simulation) School of Medicine University of Brussels B-1000 Brussels Belgium

Numerical methods for solving the diffusion equation are based on discretizing space and time so as to transform the partial differential equations into a set of ordinary differential equations or into an algebraic system. (Hybrid computers may make time or one space dimension continuous.) The purpose of this paper is to present another method, namely the stochastic method, which is derived from the physical knowledge of the diffusion process and not from the mathematical equation. The paper concludes with a comparison of the stochastic method, which may be programmed on small digital computers, with two well- known numerical methods and showing their respective advantages and disadvantages in computing time, accuracy, and ease of programming and suggests areas in which the different methods are appropriate.

SIMULATION, Vol. 25, No. 2, 33-41 (1975)
DOI: 10.1177/003754977502500202


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