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Abstract:
Mathematical models of many physical, biological, and economic processes involve systems of differential equations. The solution of such a system, in principle, can be given by an exponential function. Although exponential functions are relatively simple in many cases, such as those we see in calculus, they can be very complicated and difficult to evaluate. This presentation will focus on the issue of how an exponential function is computed when matrices are involved. Some historic notes, cutting-edge results, and applications to parallel-splitting computations will be presented.
Biographical Information:
Tim Sheng has been a professor in the Department of Mathematics. He received his Ph.D. in 1990 from the Department of Applied Mathematics and Theoretical Physics, University of Cambridge. After his study in Cambridge, he spent a year at University College London (main part of the University of London) before joining the National University of Singapore as a faculty member. Before joining Baylor, he also taught at the University of Louisiana and the University of Dayton, Ohio.
Tim's research has been in computational mathematics, in particular highly affective and accurate numerical methods for solving partial differential equations in science and engineering. His research had been funded by the NSF, State Governments, Dow Chemical Company and the U.S. Air Force. He and his students are currently working on an interface problem in infra laser optical beam propagations. He has published more than 60 papers and monographs, is currently serving in 4 journal editorial boards and is guest editor of 2 special research issues. |
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