The non-linear equal width equation is solved by Galerkin's method using linear finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found employing the Crank-Nicolson approach including a product approximation. The three invariants of the motion are calculated to determine the conservation properties of the system. L-2 and L-infinity error norms are used to measure differences between the exact and numerical solutions. The simulations of solitary wave motion are used to determine the properties of the algorithm. Finally, the development of an undular bore is studied. (C) 2003 Elsevier Inc. All rights reserved.