Abstract The improved Boussinesq equation is numerically studied using a higher-order compact finite difference technique. The aim is to achieve a mass and energy preserving scheme precisely on any time–space regions. The advantage of this scheme is that we can deal with a nonlinear partial differential equation with an implicit linear algorithm. Furthermore, the characteristics of the method are its simple steps and effective clearness. In addition, the convergence and stability analysis are then conducted to search a numerical solution whose the existence and uniqueness are guaranteed. The spatial accuracy is analyzed and found to be fourth order on a uniform grid. The numerical results are compared with established available data in literature for similar test cases, and the results are seen to be in good agreement. Besides, we perform relevant numerical simulations to illustrate the faithfulness of the present method by the evidences of the solitary wave interaction as well as the rapidly depressed solitary waves generation under sufficiently instantly decaying initial data.

中文翻译：

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高精度的紧凑结构保持算法扩展到改进的Boussinesq方程

摘要 利用高阶紧致有限差分技术对改进的Boussinesq方程进行了数值研究。目的是在任何时空区域精确地实现质量和能量保持方案。这种方案的优点是我们可以用隐式线性算法处理非线性偏微分方程。此外，该方法的特点是步骤简单，有效清晰。此外，然后进行收敛性和稳定性分析，以寻找保证存在性和唯一性的数值解。分析空间精度，发现在均匀网格上为四阶。将数值结果与类似测试案例的文献中已建立的可用数据进行比较，结果被认为具有良好的一致性。除了，