报告题目：Numerical methods for nolinear Schrödinger equations with low regularity or singularity
报 告 人： 王楚善 博士 芝加哥大学
报告时间：2025年12月2日 10:00-11:00
报告地点：线上 腾讯会议：216210076
校内联系人：张剑桥 邮箱：jqzhang22@mails.jlu.edu.cn
报告摘要：
The nonlinear Schrödinger equation (NLSE) arises from various applications in quantum physics and chemistry, laser beam propagation, plasma physics, Bose-Einstein Condensates, etc. In these applications, it is necessary to incorporate low-regularity or singularity into the NLSE through the potential, the nonlinearity, and/or the initial data. Typical examples include the discontinuous square-well potential, the singular Coulomb potential, the Lee-Huang-Yang correction term, and the logarithmic nonlinearity. Such low regularity and singularity pose significant challenges in the analysis of standard numerical methods and the development of accurate, efficient and structure-preserving numerical schemes.
In this talk, I will introduce several new analysis techniques to establish optimal error bounds for some widely used numerical methods under optimally weak regularity assumptions. Based on the analysis, we also propose novel temporal and spatial discretizations to handle the low regularity and singularity more effectively.
报告人简介：
王楚善博士，现为芝加哥大学统计系计算与应用数学Kruskal Instructor。2024年在新加坡国立大学获得博士学位。主要研究非线性色散方程的数值方法设计及误差估计, 相关成果在SIAM J. Numer. Anal., Math. Comp., SIAM J. Sci. Comput.等知名期刊上发表。
