主講人：王雨順 南京師范大學(xué)教授

時(shí)間：2022年5月25日10：00

地點(diǎn)：騰訊會(huì)議 945 830 592

舉辦單位：數(shù)理學(xué)院

主講人介紹：王雨順，南京師范大學(xué)教授、博導(dǎo)。長(zhǎng)期從事保結(jié)構(gòu)算法及其應(yīng)用研究，已經(jīng)主持7項(xiàng)國(guó)家基金委項(xiàng)目，同時(shí)作為主要成員參加科技部“863”課題、“973”項(xiàng)目、“863”計(jì)劃、基金委重點(diǎn)項(xiàng)目，入選江蘇省“333”工程、青藍(lán)工程學(xué)術(shù)帶頭人、江蘇省“六大人才高峰”高層次人才；江蘇省創(chuàng)新團(tuán)隊(duì)主持人；獲得江蘇省科學(xué)技術(shù)獎(jiǎng)，江蘇省數(shù)學(xué)成就獎(jiǎng)。專(zhuān)著《偏微分方程保結(jié)構(gòu)算法》獲得中國(guó)政府圖書(shū)獎(jiǎng)?，F(xiàn)任期刊International Journal of Computer Mathematics、《計(jì)算數(shù)學(xué)》編委，江蘇省計(jì)算數(shù)學(xué)分會(huì)秘書(shū)長(zhǎng)。

內(nèi)容介紹：In this paper, we propose a novel class of Runge-Kutta methods for the Camassa-Holm equation, 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 more than polynomial energy.