报告题目：Uniform error bounds on numerical methods for long-time dynamics of dispersive PDEs
报告人： 包维柱 教授
报告时间：2024年10月26日（周六）下午16:20-17:20
报告地点：藕舫楼 724室
主持人： 王廷春 教授
报告摘要：In this talk, I report our recent work of error estimates on different numerical methods for the long-time dynamics of dispersive PDEs with small potential or weak nonlinearity, such as the Schroedinger equation with small potential, the nonlinear Schroedinger equation with weak nonlinearity, the nonlinear Klein-Gordon equation with weak nonlinearity, the Dirac equation with small electromagnetic potential, and the nonlinear Dirac equation with weak nonlinearity, etc. By introducing a new technique of regularity compensation oscillatory (RCO), we can establish improved uniform error bounds on time-splitting methods for dispersive PDEs with small potentials and/or weak nonlinearity. This talk is based on joint works with Yongyong Cai, Yue Feng, Chunmei Su and Wenfan Yi.
报告人简介：Professor Weizhu BAO is Provost's Chair Professor at Department of Mathematics, and Vice Dean for Graduate Studies and Academic Affairs of Faculty of Science, National University of Singapore (NUS). He got his PhD from Tsinghua University in 1995 and afterwards he had postdoc and faculty positions at Tsinghua University, Imperial College in UK, Georgia Institute of Technology and University of Wisconsin at Madison in USA. He joined NUS as an Assistant Professor in 2000 and was promoted to Professor in 2009. His research interests include numerical methods for partial differential equations, scientific computing/numerical analysis, analysis and computation for problems from physics, chemistry, biology and engineering sciences. He has made significant contributions in modeling and simulation of Bose-Einstein condensation, solid-state dewetting and geometric PDEs; and in multiscale methods and analysis for highly oscillatory PDEs. He had been on the Editorial Board of SIAM Journal on Scientific Computing during 2009--2014 and is currently on the Editorial Board of SIAM Journal of Numerical Analysis. He was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. He has been invited to give plenary and/or invited talks in many international conferences including an Invited Speaker at the International Congress of Mathematicians (ICM) in 2014. He was elected a Fellow of the American Mathematical Society (AMS Fellow), a Fellow of the Society of Industrial and Applied Mathematics (SIAM Fellow) and a Fellow of Singapore National Academy of Science (SNAS Fellow) in 2022.
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数学与统计学院
江苏省应用数学（南京信息工程大学）中心
江苏省系统建模与数据分析国际合作联合实验室
2024年10月23日