The k = 1 Finite Element Numerical Solution for the Improved Boussinesq Equation

Fidel Contreras López, Eusebio Tapia, F. Ongay, M. Agüero
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引用次数: 2

Abstract

The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time; this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed; the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction; solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper; the known results in the bibliography are confirmed.
改进Boussinesq方程的k = 1有限元数值解
利用最基本的拉格朗日元k = 1,用经典有限元法求解改进的Boussinesq方程,得到一个二阶非线性常微分方程组;这可以用任何标准的精确数值方法求解,例如龙格-库塔-费贝格法。通过一个典型实例验证了该方法的有效性,并证实了该方法在空间上具有四阶收敛性;用1孤子解和2孤子解模拟波的传播、波的分裂和相互作用;溶液爆破用图形描述。本文主要使用计算机符号系统MathLab进行数值模拟;参考书目中已知的结果得到了确认。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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