NSF-CBMS Regional Research Conference, Nonstandard Finite Difference Methods: Advances in Theory and Applications

North Carolina Agricultural & Technical State University, Greensboro NC

Investigators

Abstract

This National Science Foundation award supports the 2020 NSF-CBMS conference "Nonstandard Finite Difference Methods: Advances in Theory and Applications" to be held July 20-24, 2020 at North Carolina A&T State University. The 5-day conference will feature Professor Ronald E. Mickens of Clark Atlanta University, who will deliver ten lectures on the topic, beginning with basic numerical motivations for the method, including theoretical exposition and various applications to differential equations models of diverse phenomena in the sciences, medicine, and engineering, and concluding with open problems. While the general scientific goal of the conference is the understanding and extensions of nonstandard finite difference methods (NSFD) methods that will emerge from the lectures and the discussion sessions, the human development goal is to introduce and encourage new researchers to this exciting field of research, with a focus on faculty and students from Historically Black Colleges and Universities and Minority Serving Institutes, whose activities are normally confined to teaching. The conference is intended to stimulate interest and activity in the study of NSFD methods and their applications, to be enabled by hands-on activities as well as panel discussions led by invited senior researchers on NSFD models in applications, graduate and undergraduate research projects, and a framework for future collaborations. The main conference lectures are designed to advance understanding and explore new frontiers in NSFD theory and applications of the methodology, which addresses the emergence of numerical instabilities and contrived chaotic behavior that is prevalent in standard finite difference models. Beginning with need for numerical methods for DEs, the lectures will introduce participants to the basic foundations and formulations of the NSFD methodology, discuss the state-of-the-art and latest advances in theory and applications, and summarize open problems as well as possible future directions in the field. Advances in theory will include explorations of potentially transformative concepts for generalized NSFD construction methods for systems of ordinary, partial, delay, and fractional differential equations. Advances in applications will be highlighted with various studies of engineering, science, and mathematical phenomena of classic or emerging interest modeled by the various classes of differential equations. The lectures presented by Professor Mickens, to be consolidated in a monograph, will unify these disparate research areas at their intersection and will serve as a resource to advance understanding, discovery, and inter-disciplinary collaboration in the mathematical sciences and other science and engineering disciplines. Further conference information will be available at http://www.ncat.edu/~math/cbms2020/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.