走向现代数学学术报告 - 王廷春教授（No. 945)

报告题目：Explicit and high-order accurate exponential wave integrators: derivation, analysis and application

报告时间：2026年6月18日 10:00

报告地点：东海岸校区-D实209

报 告 人：王廷春 教授（南京信息工程大学）

邀 请 人：易倩 博士

报告摘要：In this talk, we propose several novel explicit and high-order accurate exponential wave integrators. Then we apply them in time direction and adopt the Fourier pseudo-spectral method in space direction to propose several exponential wave integral Fourier pseudo-spectral (EWI-FP) methods to solve the long-time dynamics of the nonlinear Schrödinger equation with a wave operator (NLSW) under weak nonlinearity, characterized by $0<\epsilon=1$. The proposed EWI-FP methods exhibit several notable features: (1) they are completely explicit in the phase space and so are very efficient in the practical computation; (2) they are unconditionally stable and convergent with high-order accuracy in time and spectral accuracy in space; (3) they can simultaneously approximate both the exact solution and its temporal derivative at each time step. Furthermore, their optimal and uniform error estimates are rigorously established over a time period extending up to $T=O(\epsilon^{-\beta})$ with $\beta\in [0,2]$. Numerical results are reported to verify the theoretical analysis and simulate the long-time dynamics of the NLSW under weak nonlinearity.

报告人简介：王廷春，2008年博士毕业于南京航空航天大学，后至北京应用物理与计算数学研究所做博士后，2010年11月至今在南京信息工程大学工作，现为南信大数学与统计学院教授、博士生导师、计算数学团队负责人。主要从事量子力学及相场中某些偏微分方程的数值求解、地震波数值模拟和数据分析方面的研究工作，在非线性Schrödinger方程、Zakharov方程、Klein-Gordon-Dirac方程、Cahn-Hilliard方程等非线性方程（组）的有限差分法、有限元法和谱方法的算法研究方面做出一些新的学术成果。相关成果发表在Journal of Computational Physics、Journal of Scientific Computing、IMA Journal of Numerical analysis、SCIENCE CHINA Mathematics等学术期刊上，论文被引1800余次。先后主持多项国家自然科学基金和江苏省自然科学基金。科研成果和教学成果分别获得江苏省高校自然科学奖一等奖和江苏省教学成果奖一等奖。