“Nonstandard Finite Difference (NSFD) Schemes for Differential Equations: Methodology and Applications”
School of Physics Nonlinear Science and Mathematical Physics: Dr. Ronald E. Mickens, Distinguished Fuller E. Callaway Professor
NSFD schemes are based on a methodology not centered on the a priori satisfaction of particular mathematical requirements. A central and critical feature is that the discretization equations be dynamical consistent with the differential equations with regard to specific properties of the (physical) original system. Major consequences include modification of the step-size function and the non-local discrete representations of function. The general procedures will be illustrated by means of several explicit examples.
Ronald Elbert Mickens received his BA degree in physics from Fisk University (1964) and a Ph.D. in theoretical physics from Vanderbilt University (1968). He held postdoctoral positions at the MIT Center for Theoretical Physics (1968-70), Vanderbilt University (1980-81), and the Joint Institute for Laboratory Astrophysics (1981-82). He was professor of physics at Fisk University from 1970 – 1981. Presently, he is the Distinguished Fuller E. Callaway Professor at Clark Atlanta University. His current research interests include nonlinear oscillations, asymptotic methods for difference and differential equations, numerical integration of differential equations, the mathematical modeling of periodic diseases, the history/sociology of African Americans in science, and the relationship between mathematics and physics. As of 2016, he has published more than 335 peer-reviewed scientific/mathematical research articles; written and/or edited 17 books; published over 390 abstracts; and authored nearly 100 scientific bio-essays, book reviews, and commentaries. He serves on editorial boards of several research journals, including the Journal of Difference Equations and Applications and the International Journal of Evolution Equations. His scholarly writings have appeared in reference works such as African American Lives (Oxford University Press), American National Biography (Oxford University Press), and Biographical Encyclopedia of Scientists (Marshall Cavendish). His honors include fellowships from the Ford, Woodrow Wilson, and National Science Foundations; and election to Phi Beta Kappa (1964). During 1998-99, he was an American Physical Society Centennial speaker (as part of the activities to celebrate the 100th anniversary of the founding of the APS). He also served as a Distinguished National Lecturer for Sigma Xi, The Scientific Research Society for 2000 – 2002. His professional memberships include the American Association for the Advancement of Science, the American Physical Society (for which he is an elected Fellow), the History of Science Society, the Society for Mathematical Biology, and the American Mathematical Society.
In July 2014, “The Brauer-Mickens Distinguished Seminar Series,” in the Simon A. Levin Mathematical, Computational and Modeling Center (Arizona State University), was inaugurated to honor Ronald Mickens for his “stellar scholarly contributions to the mathematical, engineering, and natural sciences … and (his) overall service and mentorship to the applied mathematical sciences community.”
Access to a multi-hour interview with Professor Mickens is posted at http://www.thehistorymakers.com/biography/Ronald-n. This interview covers a variety of issues related to his family life, career, and scientific contributions. The Amistad Research Center, Tulane University, New Orleans, LA, houses a large collection of his personal and scientific correspondence.