An Introduction to Nonstandard Finite Difference (NSFD) Schemes
by
Ronald E. Mickens
Department of Physics, Clark Atlanta University, Atlanta GA 30314

NSFD schemes provide techniques to eliminate particular types of numerical instabilities which can arise in the numerical integration of differential equations. We show, by imposing the condition of "dynamic consistency, " that the NSFD methodology can generate schemes during superior numerical integration solutions as compared to standard procedures. We illustrate the application of NSFD methods by means of several examples from ordinary and partial differential equations. Various unresolved issues will also be presented. The basis for NSFD methods is the generalization of the discrete derivative and the nonlocal representation of functional terms. For a full understanding of this presentation, only knowledge of the calculus and the basic concepts of differential equations are needed.

Date received: March 13, 2007