论文标题
通用的罗塞瑙型方程
Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation
论文作者
论文摘要
在本文中，我们关注的是，分别求解广义的rosenau型方程的任意高阶动量和能量保存方案。在符号runge-kutta方法中制定了具有动量的方案的推导，并与空间中的标准傅立叶伪谱法相结合。然后，与二次辅助变量方法和符号runge-kutta方法结合在一起，以及标准的傅立叶伪谱法，我们为Rosenau方程提供了一类高阶质量和能量保护方案。最后，还讨论了广泛的数值测试和比较，以说明所提出的方案的性能。
In this paper, we are concerned with arbitrarily high-order momentum-preserving and energy-preserving schemes for solving the generalized Rosenau-type equation, respectively. The derivation of the momentum-preserving schemes is made within the symplectic Runge-Kutta method, coupled with the standard Fourier pseudo-spectral method in space. Then, combined with the quadratic auxiliary variable approach and the symplectic Runge-Kutta method, together with the standard Fourier pseudo-spectral method, we present a class of high-order mass- and energy-preserving schemes for the Rosenau equation. Finally, extensive numerical tests and comparisons are also addressed to illustrate the performance of the proposed schemes.
