| 相关介绍： | 摘要(Abstract) The nonlinear Schrödinger equation (NLSE) is one of the most widely
applicable equations in physical science, and is used to characterize
nonlinear dispersive waves, plasmas, nonlinear optics, water waves,
and the dynamics of molecules. In this talk, we present a linearized
finite difference scheme for solving nonlinear Schrödinger equations,
which is obtained based on the generalized finite-difference
time-domain method. The new scheme is shown to satisfy the discrete
analogous form of conservation law and is tested by two examples of
soliton propagation and collision. Compared with other popular
existing methods, numerical results demonstrate that the present
scheme provides a more accurate solution.
报告人简历： Dr. Weizhong Dai received his B.S. degree from National Huaqiao
University, M.S. degree from Xiamen University, and Ph.D. degree from
University of Iowa, USA. He is a McDermott International Professor of
Mathematics at Louisiana Tech University. His research interests
include numerical solutions of partial differential equations,
numerical heat transfer and bioheat transfer, numerical simulations
for bioeffect of electromagnetics, and numerical methods for
microfabrication systems, such as LCVD, melt crystallization, and
X-ray lithography. He has published three book/book chapters, over 100
research articles in refereed journals, and over 30 research articles
in international conference proceedings. He is a member of the
editorial board for several journals, and is a reviewer for various
international journals, conferences, and research foundations.
Currently, he is working on the development of numerical simulations
for hydrogen storage, which is supported by an NSF-EPSCOR grant, and
the development of numerical schemes for solving linear/nonlinear
Schrödinger equations, which is supported by an NASA-EPSCOR grant. |
