The k = 1 Finite Element Numerical Solution for the Improved Boussinesq Equation - International Journal of Modern Nonlinear Theory and Application

IJMNTA > Vol.4 No.1, March 2015

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

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DOI: 10.4236/ijmnta.2015.41006 4,468 Downloads 5,467 Views Citations

Author(s)

Fidel Contreras López¹, Eusebio Tapia², Fernando Ongay¹, Maximo Aguero³

Affiliation(s)

¹Departamento de Matematicas, Facultad de Ciencias, Universidad Autónoma del Estado de México, Toluca, Mexico.
²Facultad de Ciencias Fisicas, Universidad Nacional Mayor de San Marcos, Lima, Peru.
³Departamento de Fisica, Facultad de Ciencias, Universidad Autónoma del Estado de México, Toluca, Mexico.

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.

KEYWORDS

Boussinesq Equation, Soliton, Finite Element Method, Galerkin Method

Share and Cite:

López, F. , Tapia, E. , Ongay, F. and Aguero, M. (2015) The k = 1 Finite Element Numerical Solution for the Improved Boussinesq Equation. International Journal of Modern Nonlinear Theory and Application, 4, 88-99. doi: 10.4236/ijmnta.2015.41006.

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