Invariant-preserving difference schemes for the rotation-two-component Camassa-Holm system
Speaker
A/Prof. Qifeng Zhang
Zhejiang Sci-Tech University
Abstract

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.