Error Estimates of Numerical Methods for the Long-time Dynamics of the Nonlinear Klein-Gordon Equation
报告专家：冯悦 教授 西安交通大学
报告时间：7月24日（星期四），下午4:00-5:00
报告地点：数学学院西303
报告摘要：
In this talk, I will present the error estimates of numerical methods for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by with a dimensionless parameter. Analytical results indicate that the life-span of a smooth solution to the NKGE is at least up to the time at . Different numerical methods are adopted to discretize the NKGE and rigorous error bounds are established for the long-time dynamics. Numerical methods studied in this work include finite difference methods, exponential wave integrators and time-splitting methods with particular attentions paid on error bounds of different numerical methods explicitly depending on the mesh size , time step as well as the parameter up to the time with fixed. Extensive numerical examples are provided to confirm our error bounds and demonstrate that they are sharp. Finally, the results are extended to other dispersive partial differential equations (PDEs).
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，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。目前主持国家自然科学基金2项，省部级基金1项。
邀请人：唐庆粦
