Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation
Abstract
In this paper, we develop a novel class of arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation. With the aid of the invariant energy quadratization approach, the Camassa-Holm equation is first reformulated into an equivalent system, which inherits a quadratic energy. {The new system is then discretized} by the standard Fourier pseudo-spectral method, which can exactly preserve the semi-discrete energy conservation law. Subsequently, { a symplectic Runge-Kutta method such as the Gauss collocation method is applied} for the resulting semi-discrete system to arrive at an arbitrarily high-order fully discrete scheme. {We prove that the obtained schemes can conserve the discrete energy conservation law}. Numerical results are addressed to confirm accuracy and efficiency of the proposed schemes.
Keywords
Cite
@article{arxiv.1906.07342,
title = {Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation},
author = {Chaolong Jiang and Yushun Wang and Yuezheng Gong},
journal= {arXiv preprint arXiv:1906.07342},
year = {2019}
}
Comments
17pages, 17 figures