報告題目：QUADRATIC AUXILIARY VARIABLE RUNGE-KUTTA METHODS FOR THE CAMASSA-HOLM EQUATION
報 告 人：王雨順 教授
所在單位：南京師範大學伟德线上平台
報告時間：2022年11月19日 星期六 上午09:00-10:00
報告地點：#騰訊會議：390-462-731
校内聯系人：鄒永魁 zouyk@jlu.edu.cn
報告摘要：In this paper, we take the Camassa-Holm equation as an example to propose a novel class of Runge-Kutta methods for, which is named quadratic auxiliary variable Runge-Kutta (QAVRK) methods. We first introduce an auxiliary variable that satisfies a quadratic equation and rewrite the original energy into a quadratic functional. With the aid of the energy variational principle, the original system is then reformulated into an equivalent form with two strong quadratic invariants, where one is induced by the quadratic auxiliary variable and the other is the modified energy. Starting from the equivalent model, we employ RK methods satisfying the symplectic condition for time discretization, which naturally conserve all strong quadratic invariants of the new system. 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 symplectic RK methods to develop energy-preserving algorithms for general conservation systems with any polynomial energy.
報告人簡介：南京師範大學教授、博導。長期從事保結構算法及其應用研究，主持完成6項國家基金委項目，同時作為主要成員參加科技部“863”課題、“973”項目、“863”計劃、基金委重點項目，入選江蘇省“333”工程、青藍工程學術帶頭人、江蘇省“六大人才高峰”高層次人才；江蘇省創新團隊主持人；獲得江蘇省科技進步獎，江蘇省數學成就獎。專著《偏微分方程保結構算法》獲得第三屆中國政府出版獎-圖書獎。現任期刊International Journal of Computer Mathematics、《計算數學》編委。
