Improved Uniform Error Bounds on Time-splitting Methods for Long-time Dynamics of Dispersive PDEs
發(fā)布時間：2025-04-08
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活動主題：計算數(shù)學及其交叉學科前沿系列講座報告
報告題目：Improved Uniform Error Bounds on Time-splitting Methods for Long-time Dynamics of Dispersive PDEs
報告人：馮悅 教授 西安交通大學
邀請人：董灝
報告時間：2025年04月10日(星期四)上午9:00-12:00
報告地點：南校區(qū)會議中心121會議室
報告人簡介：馮悅，西安交通大學數(shù)學與統(tǒng)計學院教授，博士生導師。馮悅博士于2014年和2017年在浙江大學取得學士和碩士學位，于2020年在新加坡國立大學取得博士學位，隨后在新加坡國立大學及法國索邦大學從事博士后研究。馮悅博士近年來致力于色散偏微分方程的數(shù)值求解方法及分析方面的研究，主要關注長時間動力學和高振蕩問題的算法設計及誤差估計，相關工作發(fā)表在SIAM Journal on Numerical Analysis, Mathematics of Computation，Numerische Mathematik等計算數(shù)學權威學術期刊上。
報告摘要：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.
主辦單位：數(shù)學與統(tǒng)計學院
