走向现代数学学术报告 - 冯悦教授（No. 946)

报告题目：Explicit Symmetric Low-Regularity Integrator for the Nonlinear Schrodinger Equation

报告时间：2026年6月18日 13:00

报告地点：东海岸校区-D实209

报 告 人：冯悦 教授（西安交通大学）

邀 请 人：易倩 博士

报告摘要：The numerical approximation of low-regularity solutions to the nonlinear Schrodinger equation (NLSE) is notoriously difficult and even more so if structure-preserving schemes are sought. Recent works have been successful in establishing symmetric low-regularity integrators for NLSE. However, so far, all prior symmetric low-regularity algorithms are fully implicit, and therefore require the solution of a nonlinear equation at each time step, leading to significant numerical cost in the iteration. In this work, we introduce the first fully explicit (multi-step) symmetric low-regularity integrators for NLSE. We demonstrate the construction of an entire class of such schemes which notably can be used to symmetrise (in explicit form) a large amount of existing low-regularity integrators. We provide rigorous convergence analysis of our schemes and numerical examples demonstrating both the favourable structure preservation properties obtained with our novel schemes, and the significant reduction in computational cost over implicit methods.

报告人简介：冯悦，西安交通大学数学与统计学院教授，博士生导师。2020年博士后毕业于新加坡国立大学，随后在新加坡国立大学及法国索邦大学从事博士后研究，2023年入职西安交通大学数学与统计学院。冯悦博士致力于色散类偏微分方程数值求解方法及分析方面的研究，主要关注长时间动力学和高振荡问题的算法设计及误差估计，相关工作发表在SIAM J. Numer. Anal., Math. Comp., Numer. Math.等计算数学权威期刊上。