Ph.D. in Mathematics, University of Cambridge, 1990
Dr. Sheng joined the Baylor faculty in August 2005. Prior to coming to Baylor he held a research position in University of London (1989-1990), a visiting professor position in Baylor University (2003) and faculty positions in National University of Singapore (1990-1995), University of Louisiana (1996-2001) and University of Dayton (2001-2005). He was a recipient of the J. T. Knight Prize in Mathematics (1987) and Lundgren Research Award (1989). Dr. Sheng was an invited research participant of the Isaac Newton Institute for Mathematical Sciences, Cambridge, England (2007). He was a U.S. Air Force SFFP Research Fellow (2005-2007). Dr. Sheng directed two doctoral dissertations, 8 Master of Science theses and a number of undergraduate research theses. He is married to Helen. They have sons Andy and Dan. He enjoys reading, painting, traveling and spending time with the family.
Academic Interests and Research:
Dr. Sheng's research is in computational mathematics. In particular, he is interested in splitting and adaptive methods for solving singular partial differential equations. He has been involved in cross-disciplinary projects in scientific and engineering computations. Dr. Sheng has been active in his research fields and community. He is on editorial boards of several scholarly journals and special research issues. His projects have been supported by the United States Air Force Research Laboratory and Department of Defense.
Selected Research Articles:
Hybrid approximations via second order crossed dynamic derivatives with the diamond-alpha derivative, Nonlinear Anal.: Real World Appls., 9 (2008), 628-640
(with P.W. Eloe and S. Hilger) A qualitative analysis on nonconstant graininess of the adaptive grid via time scales, Rocky Mountain J. Math., 36 (2006), 115-133
(with A. Khaliq and D. Voss) Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme, Math. Computers Simulations, 68 (2005), 355-373
(with H. Cheng, P. Lin and R. Tan) Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting, SIAM J. Scientific Computing, 25 (2003), 1273-1292.
(with A. Khaliq and E. Al-Said) Solving the generalized nonlinear Schroedinger equation in quantum mechanics via quartic spline approximations, J. Comput. Physics, 166 (2001), 400-417
(with F. Farshad and S. Duan) A simulation of crystallinity gradients in injection molded PPS polymers via parallel splitting, Engineering Computations, 16 (1999) 892-912
(with T. Tang) Optimal convergence of an Euler and finite difference method for nonlinear partial integro-differential equations, Math. Comput. Modelling, 21 (1995), 1-11
Global error estimate for exponential splitting, IMA J. Numer. Anal., 14 (1993), 27-56
Solving linear partial differential equations by exponential splitting, IMA J. Numer. Anal., 9 (1989), 199-212
Adaptive Method of Lines, CRC Press, New York and London, 2001.
Dr. Sheng's teaching interests range from introductory calculus classes to specialized courses for graduate students. He has been offering individual study courses on numerical methods for partial differential equations, approximation theory and methods as well as computational finance for graduate and undergraduate students.
Courses taught at Baylor: