APPLICATION OF THE COLLOCATION METHOD WITH B-SPLINES TO THE GEW EQUATION

In this paper, the generalized equal width (GEW) wave equation is solved numerically by using a quintic B-spline collocation algorithm with two different linearization techniques. Also, a linear stability analysis of the numerical scheme based on the von Neumann method is investigated. The numerical algorithm is applied to three test problems consisting of a single solitary wave, the interaction of two solitary waves, and a Maxwellian initial condition. In order to determine the performance of the numerical method, we compute the error in the [L.sub.2] - and [L.sub.[infinity]] - norms and in the invariants [I.sub.1], [I.sub.2], and [I.sub.3] of the GEW equation. These calculations are compared with earlier studies. Afterwards, the motion of solitary waves according to different parameters is designed. Key words. GEW equation, finite element method, quintic B-spline, soliton, solitary waves AMS subject classifications. 41A15, 65N30, 76B25