TITLE:
The k = 1 Finite Element Numerical Solution for the Improved Boussinesq Equation
AUTHORS:
Fidel Contreras López, Eusebio Tapia, Fernando Ongay, Maximo Aguero
KEYWORDS:
Boussinesq Equation, Soliton, Finite Element Method, Galerkin Method
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.4 No.1,
March
25,
2015
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.