Cubic Hermite collocation solution of Kuramoto–Sivashinsky equation

Abstract

The solution and analysis of Kuramoto–Sivashinsky equation by cubic Hermite collocation method is performed and a bound for maximum norm of the semi-discrete solution is derived by using Lyapunov functional. Error estimates are also obtained for semi-discrete solutions and verified by numerical experiments.

Keywords:

• Kuramoto–Sivashinsky equation
• Lyapunov functional
• optimal estimates
• Hermite collocation method
• optimal order of convergence

2009 AMS Subject Classifications:

• 35Q53
• 65Z05
• 65G99
• 65N15
• 65N99

Acknowledgements

Mr Ishfaq Ahmad Ganaie is thankful to NBHM, Mumbai, for providing financial assistance.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work is supported by National Board of Higher Mathematics, Mumbai, INDIA in the form of research project no. 2/48(14)/2009/R&D-II/2806.