报告题目：Error estimates of numerical methods for nonlinear Schrödinger equations with low regularity or singularity

报 告 人：王楚善博士后（新加坡国立大学）

报告时间：2025年4月18日  15:00-16:00

报告地点：数学研究中心研讨室534

报告摘要：

The nonlinear Schrödinger equation (NLSE) arises from various applications in quantum physics and chemistry, nonlinear optics, plasma physics, Bose-Einstein Condensates, etc. In these applications, it is necessary to incorporate low-regularity or singular potential and nonlinearity into the NLSE. Typical examples of such potential and nonlinearity include the discontinuous square-well potential, the singular Coulomb potential, the non-integer power nonlinearity, and the logarithmic nonlinearity. Such low regularity and singularity pose significant challenges in the analysis of standard numerical methods and the development of novel accurate, efficient, and structure-preserving 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，现为新加坡国立大学数学系博士后。2024年在新加坡国立大学获得博士学位，同年获得国际科学计算与微分方程会议（Sci CADE）最佳学生报告奖（John Butcher Prize）。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., Math. Models Methods Appl. Sci.等知名期刊上发表。