In this paper, we pursue further analysis of the performance of a compact structure‐preserving finite difference scheme. The convergence, stability, and accuracy of the approximate solution with respect to grid refinement are discussed. The compact difference approach to precisely preserving invariants on any time‐space regions gives a three‐level linear‐implicit scheme with the spatial accuracy, found to be fourth order on a uniform grid. The method is verified by comparison with a solution of the Rosenau–Kawahara equation just obtained with second‐order finite difference schemes recently. Also, the efficiency of the present algorithm is confirmed by simulations of the problem at a long time. Details of CPU time are examined in order to assess the usefulness of the compact scheme for determining an approximate solution.

中文翻译：

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浅水波Rosenau–Kawahara模型的紧凑结构保形方法研究进展

在本文中，我们将对保留结构的紧凑型有限差分方案的性能进行进一步分析。讨论了关于网格细化的近似解的收敛性，稳定性和准确性。紧凑差分方法可以精确地保留任何时空区域上的不变性，从而给出具有空间精度的三级线性隐式方案，该方案在均匀网格上为四阶。通过与最近通过二阶有限差分方案获得的Rosenau-Kawahara方程的解进行比较，验证了该方法。而且，通过长时间对问题进行仿真，可以确认本算法的效率。为了评估紧凑方案确定近似解决方案的有用性，将检查CPU时间的详细信息。