数学学科Seminar第2634讲 改进的长时间分裂方法的一致误差界

创建时间:  2024/04/01  龚惠英   浏览次数:   返回

报告题目 (Title):改进的长时间分裂方法的一致误差界 (Improved Uniform Error Bounds on Time-splitting Methods for Long-time Dynamics of Dispersive PDEs)

报告人 (Speaker): 冯悦 教授 (西安交通大学)

报告时间 (Time):2024年4月10日(周三) 9:00

报告地点 (Place): 校本部D206

邀请人(Inviter):秦晓雪

主办部门:古天乐代言太阳集团数学系

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.

上一条:古天乐代言太阳集团核心数学研究所——几何与分析综合报告第70讲 各种稳定性概念之间的关系及其应用

下一条:量子科技研究院seminar第12讲暨物理学科Seminar第655讲 强关联电子系统计算方法:非平衡态动力学平均场与二粒子自洽理论


数学学科Seminar第2634讲 改进的长时间分裂方法的一致误差界

创建时间:  2024/04/01  龚惠英   浏览次数:   返回

报告题目 (Title):改进的长时间分裂方法的一致误差界 (Improved Uniform Error Bounds on Time-splitting Methods for Long-time Dynamics of Dispersive PDEs)

报告人 (Speaker): 冯悦 教授 (西安交通大学)

报告时间 (Time):2024年4月10日(周三) 9:00

报告地点 (Place): 校本部D206

邀请人(Inviter):秦晓雪

主办部门:古天乐代言太阳集团数学系

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.

上一条:古天乐代言太阳集团核心数学研究所——几何与分析综合报告第70讲 各种稳定性概念之间的关系及其应用

下一条:量子科技研究院seminar第12讲暨物理学科Seminar第655讲 强关联电子系统计算方法:非平衡态动力学平均场与二粒子自洽理论