The regularized long wave (RLW) equation is solved by a Petrov-Galerkin method using quadratic B-spline finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank-Nicolson approach involving a product approximation. The motion of solitary waves is studied to assess the properties of the algorithm. The development of an undular bore is modelled. Copyright (C) 2001 John Wiley & Sons, Ltd.