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.
翻译:在本文中,我们关注为解决普遍罗森瑙式方程式而专横高阶保持动力和节能计划,在横射龙格-库塔法以及标准的四维假光谱法中得出了保持动力计划,然后,结合四端辅助变数法和横射龙格-库塔法,以及标准的四维伪光谱法,我们为罗森瑙方程式提出了一类高阶质量和节能计划,最后,还进行了广泛的数字测试和比较,以说明拟议的计划的执行情况。