Least-squares quadratic B-spline finite element method for the regularised long wave equation Original Research Article

An approximate solution consisting of a combination of the quadratic B-spline functions is incorporated into the least-squares method. An application of this method is presented for computing the solution of the Regularised Long Wave (RLW) equation. Quadratic B-spline solution of the RLW equation leads to tridiagonal matrix system which is solved easily by using the Thomas algorithm. Performance of this scheme is tested by obtaining a solitary wave solution of the equation and by studying the development of the undular bore. Numerical results of the proposed algorithm is shown to have higher accuracy in terms of L2-error norm compared studying the migration of the solitary wave. A Fourier stability analysis of the method is investigated.