Nonstandard finite difference schemes for reaction-diffusion equations

We construct finite difference schemes for a particular class of one-space dimension, nonlinear reaction-diffusion PDEs. The use of nonstandard finite difference methods and the imposition of a positivity condition constrain the schemes to be explicit and allow the determination of functional relations between the space and time step-sizes. The general procedure is illustrated by applying it to several important model systems of PDEs © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 201–214, 1999