Analysis of IMEX and Time-Splitting Schemes for the Logarithmic Schrodinger’s Equation

主讲人：王立联 新加坡南洋理工大学教授

时间：2023年5月17日19：00

地点：三号楼301室

举办单位：数理学院

主讲人介绍：王立联，新加坡南洋理工大学教授，博士生导师。主要研究领域为解偏微分方程数值解，电磁学中的高性能计算方法等。在SIAM J. Numer. Anal., SIAM J. Appl. Math., SIAM J. Sci. Comput., Math. Comp.等国际知名计算数学期刊上发表论文100余篇，由Springer出版合著《SPECTRAL METHODS: Algorithms, Analysis and Applications》。

内容介绍：The Schrodinger’s 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 scheme and time-splitting scheme and on the introduction of new tools for the error analysis.