报告题目 (Title)：Explicit Symmetric Low-Regularity Integrator for the Nonlinear Schrodinger Equation（非线性薛定谔方程的显式对称低正则性积分方法）
报告人 (Speaker)：冯悦 教授 (西安交通大学)
报告时间 (Time)：2025年4月27日（周日） 10:30
报告地点 (Place)：校本部Gj303
邀请人(Inviter)：秦晓雪
主办部门：理学院数学系
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.
