Analysis of IMEX and Time-Splitting Schemes for the Logarithmic Schrodinger Equation
Abstract: The Schrodinger equation with a logarithmic nonlinear term (LogSE): f(u)=u log(|u|^2) exhibits many distinct features and rich dynamics that make it unique among nonlinear wave equations. However, such a nonlinearity presents significant challenges in both numerical solutions and analysis. Compared with usual cubic case, the nonlinear term f(u) is non-differentiable at u=0 but only possesses certain Holder continuity. In this talk, we shall report our recent attempts in numerical study of the LogSE with a focus on time discretization via implicit-explicit (IMEX) scheme and time-splitting scheme and on the introduction of new tools for the error analysis. This talk is based on joint works with Jingye Yan (Jiangsu University) and Xiaolong Zhang (Hunan Normal University).
Biography:Professor Li-Lian Wang is currently a full Professor of Nanyang Technological University (NTU) in Singapore. He received his PhD from Shanghai University in 2000. Before he joined NTU as an Assistant Professor in 2006, he worked as a Visiting Assistant Professor and Postdoctoral Fellowin Purdue University since 2002. He was the Min Jiang Chair Professor of Xiamen University from 2016 to 2019. His main research interest resides in the spectral/high-order methods and computational acoustics & electromagnetics. His recent research focus lies in singular and nonlocal PDEs. He has published more than 100 high-quality journal papers. His co-authored book on Spectral Methods in Springer (2011) has far-reaching impact in the scientific computing, which has more than 2000 citations to date. Some of his work has been cited and used by Fields Medalist. The algorithm on well-conditioned collocation methods developed by him has been populated into some optimal control toolbox.