4.6 Article

Arbitrarily High-Order Energy-Preserving Schemes for the Zakharov-Rubenchik Equations

期刊

JOURNAL OF SCIENTIFIC COMPUTING
卷 94, 期 2, 页码 -

出版社

SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-022-02075-4

关键词

Zakharov-Rubenchik equations; Energy-preserving scheme; Symplectic Runge-Kutta method; Quadratic auxiliary variable approach; Fourier pseudo-spectral method

向作者/读者索取更多资源

In this paper, a novel class of high-order energy-preserving schemes for solving the Zakharov-Rubenchik equations is proposed. The schemes introduce a quadratic auxiliary variable to transform the Hamiltonian energy and reformulate the original system into an equivalent system satisfying multiple invariants. The schemes achieve high-order accuracy in time and conserve the mass, Hamiltonian energy, and two linear invariants.
In this paper, we present a novel class of high-order energy-preserving schemes for solving the Zakharov-Rubenchik equations. The main idea of the scheme is first to introduce an quadratic auxiliary variable to transform the Hamiltonian energy into a modified quadratic energy and the original system is then reformulated into an equivalent system which satisfies the mass, modified energy as well as two linear invariants. The symplectic Runge-Kutta method in time, together with the Fourier pseudo-spectral method in space is employed to compute the solution of the reformulated system. The main benefit of the proposed schemes is that it can achieve arbitrarily high-order accurate in time and conserve the three invariants: mass, Hamiltonian energy and two linear invariants. In addition, an efficient fixed-point iteration is proposed to solve the resulting nonlinear equations of the proposed schemes. Several experiments are addressed to validate the theoretical results.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.6
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据