报告题目：Notes on Exponential Splitting and Their Applications for the Numerical Solution of Singular Reaction-Diffusion Equations
报告人：Prof. Qin Sheng
Department of Mathematics
Center for Astrophysics, Space Physics and Engineering Research (CASPER Baylor University Texas, USA
报告时间：2017年5月11日（周四）9:20
报告地点：尚贤楼706会议室
Abstract:
This talk consists of two interactive components. First, we will pay an attention to existing splitting methods, such as the non-exponential ADI and exponential LOD methods, and explore their modernizations. Then we will focus at interesting issues involving the design and analysis of highly-effective and highly-efficient finite difference methods for solving singular reaction-diffusion equations which are important to various scientific applications including biology and bio-medicine. We will outline the physical background of the quenching phenomena related. Basic adaptive finite difference approaches will be introduced. Numerical analysis on their monotonicity, convergence and stability will be discussed. We will also discuss the latest exponential evolving grid development inspired by moving grid strategies. The general idea of such adaptations can be extended for solving similar multiphysics equations emerging from studies of biophysics, oil pipeline decay detection and laser-materials interactions. Certain stochastic inferences will be involved. Potentials of further investigations and collaborations will be discussed together with Professor You.
About Prof. Qin Sheng:
Dr. Sheng received his BS and MS in Mathematics from Nanjing University in 1982, 1985, respectively. Then he acquired his Ph.D. from DAMTP, University of Cambridge under the supervision of Professor Arieh Iserles. After his postdoctoral research with Professor Frank T. Smith, FRS, in University College London, he joined National University of Singapore in 1990. Since then, Dr. Sheng was on faculty of several major universities till his joining Baylor University, which is one of known research institutions and the second biggest private university in the United States. Dr. Sheng has been interested in splitting and adaptive numerical methods for solving linear and nonlinear partial differential equations. He is also known for the Sheng-Suzuki theorem in numerical analysis. He has published over 100 refereed articles as well as several joint research monographs. He has been an Editor-in-Chief of an SCI journal, International Journal of Computer Mathematics, published by Taylor and Francis since 2010. He gives invited presentations, including keynote lectures, in international conferences every year. Dr. Sheng's projects have been supported by several U.S. research agencies. He currently advises 3 doctoral students and 1postdoctoral research fellow.
