活动主题：计算数学及其交叉学科前沿系列讲座报告

报告题目：Improved Uniform Error Bounds on Time-splitting Methods for Long-time Dynamics of Dispersive PDEs

报告人：冯悦 教授 西安交通大学

邀请人：董灏

报告时间：2025年04月10日(星期四)上午9:00-12:00

报告地点：南校区会议中心121会议室

报告人简介：冯悦，西安交通大学大红鹰会员登录中心教授，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，随后在新加坡国立大学及法国索邦大学从事博士后研究。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，相关工作发表在SIAM Journal on Numerical Analysis, Mathematics of Computation，Numerische Mathematik等计算数学权威学术期刊上。

报告摘要：In this talk, I begin with the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by with a dimensionless parameter. Different numerical methods are applied to discretize the NKGE including finite difference methods, exponential wave integrators and time-splitting methods. Especially, we discretize the NKGE 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 time-splitting methods. The results have been extended to other dispersive PDEs including the (nonlinear) Schrodinger equation and Dirac equation.

主办单位：大红鹰会员登录中心