报告题目：Quadratic-auxiliary variable Runge-Kutta method for the Camassa-Holm equation
主讲人：王雨顺教授（南京师范大学）
时间：2023年10月14日（周六）10:00 a.m.
地点：北院卓远楼305会议室
主办单位：统计与数学学院
摘要：In this talk, we take the Camassa-Holm equation as an example to propose a novel class of Runge-Kutta methods for conservative systems, which is named quadratic auxiliary variable Runge-Kutta (QAVRK) methods. The resulting methods are shown to inherit the relationship between the auxiliary variable and the original one, and thus can be simplified by eliminating the auxiliary variable, which leads to a new class of QAVRK schemes. Furthermore, the QAVRK methods are proved rigorously to preserve the original energy conservation law. Numerical examples are presented to confirm the expected order of accuracy, conservative property and efficiency of the proposed schemes. This numerical strategy makes it possible to directly apply the SRK methods to develop energy-preserving algorithms for general conservation systems with any polynomial energy.
主讲人简介：
王雨顺，南京师范大学教授、博导。长期从事保结构算法及其应用研究，主持完成6项国家基金委项目，同时作为主要成员参加科技部“863”课题、“973”项目、“863”计划、 基金委重点项目，以第一完成人获得教育部自然科学奖二等奖，入选江苏省“333”工程、 青蓝工程学术带头人、江苏省“六大人才高峰”高层次人才；江苏省创新团队主持人；获得江苏省科技进步奖，江苏省数学成就奖。专著《偏微分方程保结构算法》获得第三届中国政府出版奖-图书奖。现任期刊International Journal of Computer Mathematics、《计算数学》编委。江苏省数学学会计算数学分理事长。
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