Least-squares quadratic B-spline finite element method for the regularisedlong wave equation

An approximate solution consisting of a combination of the quadratic B-spli ne functions is incorporated into the least-squares method. An application of this method is presented for computing the solution of the Regularised L ong Wave (RLW) equation. Quadratic B-spline solution of the RLW equation le ads to tridiagonal matrix system which is solved easily by using the Thomas algorithm. Performance of this scheme is tested by obtaining a solitary wa ve solution of the equation and by studying the development of the undular bore, Numerical results of the proposed algorithm is shown to have higher a ccuracy in terms of L-2-error norm compared studying the migration of the s olitary wave. A Fourier stability analysis of the method is investigated. ( C) 2000 Elsevier Science S.A. All rights reserved.