Numerical simulations of the Boussinesq equation by He's variational iteration method

Abstract

In this paper, we present a reliable algorithm to study the well-known model of nonlinear dispersive waves proposed by Boussinesq. We solve the Cauchy problem of Boussinesq equation using variational iteration method (VIM). The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that VIM is a powerful mathematical tool for solving nonlinear problems.

Keywords:

• variational iteration method
• Lagrangian multiplier
• nonlinear dispersive waves model
• bad Boussinesq equation
• good Boussinesq equation

AMS Subject Classification :

• 35A15
• 37M05
• 49M27
• 70G75
• 35F25

Acknowledgements

The authors would like to express sincere thanks to the referees for their useful comments and discussions.