Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition

An essential feature of nonstandard finite difference schemes for differential equations is the precise manner in which the discretization of derivatives is made. We demonstrate, for differential equations modeling systems where the solutions satisfy a positivity condition, that procedures can be formulated to calculate the so‐called denominator functions that appear in the discrete derivatives. These procedures are applied to a number of both ordinary and partial model differential equations to illustrate their use.