Abstract
A finite difference scheme is constructed for the Fisher partial differential equation having a nonlinear diffusion term. The application of nonstandard methods and the requirement of a positivity condition leads to a discrete model having many of the dynamical properties of the original differential equation. In particular, the fixed-points have the same linear stability properties as those in the differential equation. Further, the scheme can be rewritten in an explicit form with a definite relation existing between the time and space step-sizes.