The <i>k</i>= 1 Finite Element Numerical Solution for the Improved Boussinesq Equation

• 作者: Eusebio Tapia Fernando Ongay Fidel Contreras López Maximo Aguero
• 来源期刊: 现代非线性理论与应用(英文)
• 学科: 数学
• 关键词: BOUSSINESQ Equation Soliton Finite Element METHOD Galerkin METHOD
• 年，卷（期）: 2015,（1）
• 页码范围: 88-99
• 页数: 12页
• 分类号: O1

摘要

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.