A B-SPLINE FINITE-ELEMENT METHOD FOR THE REGULARIZED LONG-WAVE EQUATION

A B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method w ith quadratic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solutio n range. Time integration of the resulting system of ordinary differen tial equations is effected using a Crank-Nicolson approximation. Stand ard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.