報告題目：Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs
報 告 人：李東方教授
所在單位：華中科技大學數學與統計學院
報告時間：2022年9月11日 星期日 下午15:00-16:00
報告地點：#騰訊會議：798-557-438
校内聯系人：鄒永魁 zouyk@jlu.edu.cn
報告摘要： Spatial discretizations of time-dependent partial differential equations usually result in a large system of semi-linear and stiff ordinary differential equations. Taking the structures into account, we develop a family of linearly implicit and high order accurate schemes for the time discretization, using the idea of implicit-explicit RungeKutta methods and the relaxation techniques. The proposed schemes are monotonicitypreserving/conservative for the original problems, while the previous linearized methods are usually not. We also discuss the linear stability and strong stability preserving (SSP) property of the new relaxation methods. Numerical experiments on several typical models are presented to confirm the effectiveness of the proposed methods.
報告人簡介：李東方，華中科技大學數學與統計學院教授，博導，中國系統仿真學會仿真算法專業委員會委員。曾先後赴加拿大McGill大學，香港城市大學從事博士後研究。主要從事微分方程數值解、系統仿真和信号處理等領域的研究。在微分方程保結構算法和分數階微分方程的高效數值算法和理論上取得一些有意義的進展。在SIAM系列雜志、《Math. Comput》、《J. Comp. Phys.》、《J. Sci. Comput.》等雜志上發表多篇SCI論文，多篇為高被引論文。主持國家自然科學基金、科技部項目等4項。
