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

报告时间：2024-01-09  15:30-16:30

报 告 人：冯悦  教授  西安交通大学

报告地点：理学院东北楼302

Abstract：In this talk, I begin with the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by ε^2with ε∈(0, 1] 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.