Different Differences: An Introduction to Nonstandard Finite Difference Schemes

From Calculus we know that a derivative of a function can be approximated using a
difference quotient. There are different forms of the difference quotient, such as the
forward difference (most common), backward difference (less common) and centered
difference (more accurate). In this talk I will discuss several different differences,
specifically nonstandard finite differences (NFSD) that can be used to approximate the
derivatives that appear in differential equations as a solution technique. Many NSFD
schemes have been created, discovered, and promoted by Dr. Ronald E. Mickens, an
African American Emeritus Professor of Physics at Clark Atlanta University, who has
written more than 300 research articles and a dozen books. I’ll provide examples of
NSFD schemes that can be used to solve a wide variety of problems drawn from
several different areas, such as first-semester Calculus, elementary ordinary differential
equations, and more advanced differential equations.