报告专家：西安交通大学数学与统计学院教授 冯悦

报告时间：2025年1月3日 10:00-11:00

报告地点：上海师范大学徐汇校区西区3号楼301

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.

专家简介：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。

欢迎老师们和同学们参加！

上海师范大学数理学院