Solitary-wave propagation and interactions for the ‘good’ Boussinesq equation

Abstract

A third-order rational approximant in a three-time level reccurence relation is applied successfully to the ‘good’ Boussinesq equation, already known in the literature. The resulting nonlinear finite-difference scheme, which is analysed for stability, is solved using a predictor–corrector (P–C) scheme, in which the predictor and corrector are both explicit schemes. This P–C scheme is accelerated by a modifed P–C (MPC) in which the already evaluated values are used for the corrector. The behaviour of both the P–C and MPC schemes is tested numerically on the single- and double-soliton waves, and the results from the experiments are compared with that in the literature.

Keywords:

• Boussinesq equation
• finite-difference method
• predictor–corrector

2000 AMS Subject Classification :

• 35Q51
• 35Q53
• 65M06
• 78M20
• 65Y10

Acknowledgements

This research was co-funded 75% by EU and 25% by the Greek Government under the framework of the Education and Initial Vocational Training Program – Archimedes, Technological Educational Institution (T.E.I.) Athens project ‘Computational Methods for Applied Technological Problems’.

Additional information

Notes on contributors

A. G. Bratsos

Email: [email protected]