This National Science Foundation award supports for the NSF-CBMS Conference "Nonstandard Finite Difference Methods: Advances in Theory and Applications " to be held during 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 of 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 HBCU/MI faculty, 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 and panel discussions led by invited senior researchers. 

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 NSFD 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. 


In lieu of a CBMS monograph, a CBMS Conference Edited Volume will be published containing selected contributions by participants, with Professor Mickens providing an introductory chapter on the general NSFD methodology; a complete record of Professor Mickens’s presentation will also be posted online. 

Travel Support

NSF funding permits the support of conference-associated travel and lodging costs for a limited number of participants. To stimulate research activity among these groups, graduate students, young researchers, members of underrepresented minorities, and HBCU/MI faculty are especially encouraged to apply. 

Further conference and registration information as well as an application for support will be published soon; meanwhile, if you have questions please e-mail Professor Clemence at: clemence@ncat.edu