The aim of this paper is to investigate numerical solutions of modified improved Boussinesq (MIBq) equation $u_{tt}=u_{xx}+\alpha {\left(u^3\right)}_{xx}+u_{xxtt}$, which is a modified type of Boussinesq equations born as an art of modelling water‐wave problems in weakly dispersive medium such as surface waves in shallow waters or ion acoustic waves. For this purpose, Lumped Galerkin finite element (LGFE) method, an effective, accurate, and cost‐effective method, is applied to model equation by the aid of quadratic B‐spline basis. The efficiency and accuracy of the method are tested with two problems, namely, propagation solitary wave and interaction of two solitary waves. The error norms L₂ and L_∞ have been computed in order to measure how “accurate” the numerical solutions. Also, the stability analysis has been investigated.

中文翻译：

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改进的改进的Boussinesq方程的Galerkin有限元动力学

本文的目的是研究改进的改进的Boussinesq（MIBq）方程的数值解 ${ü}_{ŤŤ}={ü}_{XX}+\alpha {\left({ü}^3\right)}_{XX}+{ü}_{XXŤŤ}$，这是Boussinesq方程的一种修改类型，它是对弱分散介质中的水波问题建模的一种艺术，例如浅水中的表面波或离子声波。为此，借助于二次B样条曲线，将集总Galerkin有限元（LGFE）方法（一种有效，准确且经济高效的方法）应用于模型方程。对该方法的有效性和准确性进行了测试，存在两个问题，即传播孤立波和两个孤立波的相互作用。误差规范大号₂和大号_∞已计算，以便测量如何“准确”的数值解。另外，已经对稳定性分析进行了研究。