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http://dx.doi.org/10.1016/S0045-7825(97)00211-9

has been cited by the following article:

• 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.