G. Kaniadakis et Pp. Delsanto, A LOCAL INTERACTION SIMULATION APPROACH TO THE SOLUTION OF DIFFUSION-PROBLEMS, Mathematical and computer modelling, 17(10), 1993, pp. 31-42
A technique for the solution of the master equation and of the diffusi
on equation, via a random walk simulation, is proposed and applied to
a variety of problems of interest in the fields of physics, biology, a
nd chemistry. They include the kinetics of a single particle, which ca
n diffuse along a one-dimensional lattice and eventually leave it from
its end points, with a given probability, and the generalization to m
ore complex two-dimensional geometries or more particles (the many-wal
kers problem). The technique is particularly suitable for parallel pro
cessing, which provides extreme efficiency and flexibility to the meth
od.