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Professor of Mathematics

Casper Faculty

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**Qualifications:**

Ph.D. in Mathematics, University of Cambridge, 1990

**Biography:**

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

**Book Chapter:**

Adaptive Method of Lines, CRC Press, New York and London, 2001.

**Teaching Interests:**

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:**

- MTH 1321 - Calculus I
- MTH 1322 - Calculus II
- MTH 3325 - Differential Equations
- MTH 4322 - Numerical Analysis
- MTH 4328 - Numerical Linear Algebra
- MTH 4V90 - Special Topics in Mathematics
- MTH 6352 - Finite Difference Methods
- MTH 6V24 - Numerical Methods for Partial Differential Equations
- MTH 6V28 - Computational Finance
- MTH 6V99 - Ph.D. Dissertation
- Honor's College - Honor's Research Projects in Mathematics