In many branches of science and engineering, a differential equation provides a model for the
problem of study. Unfortunately, most differential equations cannot be solved exactly so approximation
schemes via discretized equations are often used. This talk aims to serve two goals. First, we introduce
the Nonstandard Finite Difference Scheme, a new type of difference equation that seeks to improve
numerical accuracy by incorporating the features of the differential equation into the numerical scheme.
Second, we discuss several applications to real-world problems such as population growth, infectious
disease propagation, and economics. This is joint work in progress with Ronald Mickens.
This talk is delivered by the AWM and SIAM student chapter guest. BIO: Dr. Talitha Washington is an Associate Professor of Mathematics at Howard University. She has been
an Assistant Professor of Mathematics at the University of Evansville and The College of New Rochelle,
and a VIGRE Research Associate in the Department of Mathematics at Duke University. She earned her
master's and doctoral degrees in mathematics from the University of Connecticut, and completed her
undergraduate studies in mathematics at Spelman College. Dr. Washington's current fields of interest
include applying ordinary and partial differential equations to problems in biology and engineering.
Currently, she serves on the Executive Board of the Association for Women in Mathematics (AWM).