汇报标题 (Title)：改进的长功夫割裂步骤的一致误差界 （Improved Uniform Error Bounds on Time-splitting Methods for Long-time Dynamics of Dispersive PDEs）
汇报人 (Speaker)： 冯悦 教授 (西安交通大学)
汇报功夫 (Time)：2024年4月10日（周三） 9:00
汇报地址 (Place)： 校本部D206
约请人(Inviter)：秦晓雪
主办部门：理学院数学系
汇报提要：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.
