报告人：张晓龙（湖南师范大学）

报告时间：2026年4月10日（星期五）9:00-10:30

报告地点：科技楼南楼702室

报告摘要：In this talk, we present several numerical methods for solving the nonlinear Schrödinger equation (NLSE) within a low-regularity framework, including logarithmic and semi-smooth nonlinearities. Compared to the cubic NLSE, low-regularity models exhibit distinct dynamical behaviors and may involve singular or semi-smooth nonlinear terms, posing significant challenges for both analysis and computation. In particular, the limited regularity of the nonlinearities may lead to order reduction in classical error estimates.To address these issues, we develop some techniques and analyze a class of numerical schemes, including IMEX methods, time-splitting spectral methods, and exponential wave integrator (EWI) methods, which are well suited to low-regularity settings. We then establish rigorous error bounds that avoid order degradation and ensure the accuracy of the proposed methods.

报告人简介：张晓龙，湖南师范大学副教授。2019年毕业于大连理工大学，获博士学位；2017.01–2018.07 在密歇根大学联合培养，师从谱方法领域著名专家 John P. Boyd 教授；2022.03–2024.09 在南洋理工大学从事博士后研究，合作导师为谱方法专家 Li-Lian Wang 教授。主要从事偏微分方程数值方法研究，尤其是谱方法及其在低正则问题中的应用。已在 Math. Comp.、SIAM J. Numer. Anal.、ESAIM: M2AN、Sci. China Math. 等期刊发表论文多篇。现主持国家自然科学基金面上项目、青年项目以及省自然科学基金面上、青年项目等多项科研课题。

邀请人：王海永