A simple model of diffusion

Written by Paul Bourke
January 1993

A simple model of diffusion in a 1 dimensional strip xt(i) is as follows

xt+1(i) = D xt(i-1) + (1 - 2 D) xt(i) + D xt(i+1)

This gives the value at element i at time t+1 where D is the coefficient of diffusion, normally 0 < D << 1.

As an example, consider how a single point diffuses in time. In the following image time runs down the screen.