Application of the collocation method with b-splines to the gew equation

Abstract

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 L2- and L∞ norms and in the invariants I1, I2, and I3 of the GEW equation. These calculations are compared with earlier studies. Afterwards, the motion of solitary waves according to different parameters is designed