A B-spline finite element method is used to solve the equal width equation numerically. This approach involves a collocation method using quintic B-splines at the knot points as element shape. Time integration of the resulting system of ordinary differential equations is effected using the fourth order Runge-Kutta method, instead of the finite difference method, the resulting system of ordinary differential equations is integrated with respect to time. Standard problems are used to validate the algorithm which is then used to model the smooth development of an undular bore.