Non-polynomial splines method for numerical solutions of the regularized long wave equation

Abstract

In this paper, we construct a numerical method based on cubic splines in tension for solving regularized long wave equation. The truncation error is analysed and the method shows that by choosing suitably parameters we can obtain various accuracy schemes. Numerical stability of the method has been studied by using a linearized stability analysis. Test problems are dealt with. The numerical simulations can validate and demonstrate the advantages of the method.

Keywords:

• regularized long wave equation
• von Neumann technique
• cubic splines in tension
• solitary waves

2000 AMS Subject Classifications:

• 65D07
• 65D05

Acknowledgements

The authors thank the editor and the reviewers for their valuable comments and suggestions to improve the results of this paper.