In this talk, we develop, analyze and numerically test two classes of invariant-preserving difference schemes for a rotation-two-component Camassa-Holm system [L. Fan, H. Gao, Y. Liu, Adv. Math. (2016), pp. 59--89], which contains strongly nonlinear terms and high-order derivative terms. We prove that both the numerical schemes are uniquely solvable and second-order convergent for  the spatial and temporal discretizations. Optimal error estimates for the velocity in the $L^{\infty}$-norm and for the surface elevation in the $L^2$-norm are obtained. Extensive numerical experiments verify the convergence results as well as conservation.

张启峰, 副教授。2014年在华中科技大学获得理学博士学位。随后进入浙江理工大学担任专任教师至今，2020-2021年在洛桑联邦理工访问Jan S. Hesthaven一年。当前主要研究内容包括：非线性水波方程和分数阶微分方程的数值分析与模拟。主持完成国家自然科学基金青年基金1项，博士后基金1项。