Computational Partial Differential Equations: An Introduction and a Few Applications in Biology

Prof. Chi-Wang Shu
Division of Applied Mathematics
Brown University

Room 610, CBI, New Life Science Building, PKU
3:00 PM, Monday, 5 September,2005

Abstract:

In this talk we will first give a short introduction to partial differential equations, including mathematical modeling which leads to the derivation of partial differential equations. We will then describe general principles of numerical approximations to the solutions of partial differential equations, with an emphasis on hyperbolic equations containing discontinuous solutions. We will introduce basic ideas of a few modern high order accurate numerical schemes for hyperbolic equations. Finally, we will present a few applications in biology, including ionic channel simulation, chemosensitive movement, and a hierarchical size- structured model.

Speaker Bio:

Chi-Wang Shu received his B.Sc. degree in mathematics from the University of Science and Technology of China in 1982 and his Ph.D. degree in mathematics from UCLA in 1986. Since 1987 he has been at the Division of Applied Mathematics of Brown University, as an assistant professor (1987-91), associate professor (1992-96), professor (1996- now) and chairman (1999-2005). His research interest is in numerical solutions for partial differential equations, especially non-oscillatory high order numerical methods for convection dominated partial differential equations. He has worked on total variation bounded methods, total variation diminishing high order Runge-Kutta time discretizations, essentially non-oscillatory (ENO) and weighted ENO (WENO) finite difference and finite volume methods, discontinuous Galerkin methods, and spectral methods for discontinuous problems, with applications in computational fluid dynamics, semiconductor device simulations, traffic flow problems, astrophysics, biology, and other areas. He is the managing editor of the American Mathematical Society journal Mathematics of Computation, the co-chief editor of the Journal of Scientific Computing, and he serves in the editorial boards of 11 other journals. He is an ISI Highly Cited Author in Mathematics by ISI Web of Knowledge, and received the first Feng Kang Prize of Scientific Computing in 1995. He is a Changjiang Lectureship Professor at the University of Science and Technology of China since 2000, an Overseas Assessor of the Chinese Academy of Sciences since 2001, and a Distinguished Visiting Professor in the Academy of Mathematics and System Sciences of the Chinese Academy of Sciences since 2002.