Abstract In this paper, an energy stable time-stepping method using the finite difference approximation in time and Fourier pseudo-spectral method in space is developed for the symmetric regularized long wave equation with damping mechanism. Based upon a careful treatment of nonlinear term, the suggested numerical scheme is proved to preserve energy dissipation at discrete time levels. The energy stable property implies the priori estimates of the numerical solution. The maximum norm error estimate shows that the proposed numerical scheme is of second-order accuracy in time and spectral accuracy in space. Several numerical experiments are presented to show the effectiveness of our numerical method and to confirm our theoretical analysis.

中文翻译：

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具有阻尼机制的对称正则化长波方程的耗散有限差分傅立叶伪谱方法

摘要 本文针对具有阻尼机制的对称正则化长波方程，提出了一种利用时间上的有限差分近似和空间上的傅立叶伪谱方法的能量稳定时间步长方法。基于对非线性项的仔细处理，建议的数值方案被证明可以在离散时间级别保持能量耗散。能量稳定特性意味着数值解的先验估计。最大范数误差估计表明，所提出的数值方案在时间上具有二阶精度，在空间上具有谱精度。提出了几个数值实验，以显示我们的数值方法的有效性并证实我们的理论分析。