A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines

Abstract

The numerical solution of the one-dimensional modified equal width wave (MEW) equation is obtained by using a lumped Galerkin method based on quadratic B-spline finite elements. The motion of a single solitary wave and the interaction of two solitary waves are studied. The numerical results obtained show that the present method is a remarkably successful numerical technique for solving the MEW equation. A linear stability analysis of the scheme is also investigated.

Keywords:

• MEW equation
• Lumped Galerkin method
• Splines
• Solitary waves

Acknowledgements

The author would like to thank the anonymous referees for their valuable comments on this paper.

Additional information

Notes on contributors

A. Esen

Email address: [email protected]