Improved Uniform Error Bounds on Numerical Methods for Long-time Dynamics of the Nonlinear Schrodinger Equation

发布时间：2024-11-21 作者：浏览次数：

Speaker:	冯悦	DateTime:	2024年11月22日（周五）下午 4:30-5:30
Brief Introduction to Speaker: 冯悦，西安交通大学数学与统计学院教授，博士生导师。冯悦博士于2014年和2017年在浙江大学取得学士和硕士学位，于2020年在新加坡国立大学取得博士学位，师从包维柱教授，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年获批国家海外优青项目。冯悦博士近年来致力于色散偏微分方程的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，相关成果发表在SIAM Journal on Numerical Analysis, Mathematics of Computation等计算数学领域权威期刊上。		Place:	国交2号楼315会议室
Abstract:In this talk, I will introduce the long-time problem for the nonlinear Schrodinger equation (NLSE) with weak nonlinearity, which is characterized by ε^2 with ε∈(0,1] a dimensionless parameter. We discretize the NLSE by the second-order time-splitting method in time and combine with the Fourier spectral method in space. By introducing a new technique—Regularity Compensation Oscillation (RCO) which controls the high frequency modes by the regularity of the exact solution and analyzes the low frequency modes by phase cancellation and energy method, we carry out the improved uniform error bounds for the TSFP method. In addition, we design new exponential integrators for the low-regularity initial data and establish the improved uniform error bounds in the long-time regime.

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