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

活動主題：計算數(shù)學(xué)及其交叉學(xué)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(xué)

邀請人：董灝

報告時間：2025年04月17日(星期四)10:30-13:30

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(xué)數(shù)學(xué)與統(tǒng)計學(xué)院教授，博士生導(dǎo)師，入選國家級青年人才。馮悅博士于2014年和2017年在浙江大學(xué)取得學(xué)士和碩士學(xué)位，于2020年在新加坡國立大學(xué)取得博士學(xué)位，隨后在新加坡國立大學(xué)及法國索邦大學(xué)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(guān)注長時間動力學(xué)和高振蕩問題的算法設(shè)計及誤差估計，相關(guān)工作發(fā)表在SIAM Journal on Numerical Analysis，Mathematics of Computation，Numerische Mathematik等計算數(shù)學(xué)權(quán)威學(xué)術(shù)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(xué)與統(tǒng)計學(xué)院