Title: Collocation method using cubic B-spline for the generalised equal width equation

Authors: K.R. Raslan

Addresses: Faculty of Science, Department of Mathematics, Al-Azhar University, 11884 Nasr-City Cairo, Egypt

Abstract: The generalised equal width wave (GEW) equation ut + εupux - δuxxt = 0 is solved numerically by a B-spline finite element method. The approach used, is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. In this research, the scheme of the equation under investigation is found to be unconditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, the Maxwellian initial condition pulse is studied.

Keywords: GRLW; GKdV; cubic B-spline; solitons; generalised equal width equation; GEW; generalised regularised long wave equation; collocation method.

DOI: 10.1504/IJSPM.2006.009019

International Journal of Simulation and Process Modelling, 2006 Vol.2 No.1/2, pp.37 - 44

Published online: 12 Feb 2006 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article

 

Return to top