Numerical solutions of the equal width equation by trigonometric cubic B‐spline collocation method based on <scp>Rubin–Graves</scp> type linearization
Nuri Murat Yağmurlu, Ali Sercan Karakaş
Abstract
Abstract In this article, the equal width (EW) equation is going to be solved numerically. In order to show the accuracy of the presented method, six test problems namely single solitary wave, interaction of two solitary waves, interaction of three solitary waves, Maxwellian initial condition, undular bore, and soliton collision are going to be solved. For the first test problem, since it has exact solution, the error norms L 2 and L ∞ are going to be calculated and compared with some of the earlier studies existing in the literature. Moreover, the three invariants I 1 , I 2 , and I 3 of the given problems during the simulations are calculated and tabulated. Besides those comparisons, the relative changes of the invariants are given. Finally, a comparison of those error norms and invariants has clearly shown that the present approach obtained compatible and better results than most of the earlier works by using the same parameters.