title: A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline.
abstract: In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms [Formula: see text] and [Formula: see text] and the conservative quantities [Formula: see text], [Formula: see text] and [Formula: see text] are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.
authors.affiliation: Department of Applied Mathematics, Faculty of Computer Science, Abdullah Gul University, 38080 Kayseri, Turkey.
authors.forename: Halil
authors.initials: H
authors.lastname: Zeybek
authors.affiliation: Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University, 50300 Nevsehir, Turkey.
authors.forename: S Battal Gazi
authors.initials: SB
authors.lastname: Karakoç
keywords: Cubic B-spline; GRLW equation; Lumped Galerkin method; Solitary waves; Undular bore