The equal width equation has been solved numerically using the Galerkin finite-element method, based on the Adams-Moulton method for time integration and quadratic/cubic B-splines for space integration. The two proposed algorithms are tested on the problems of propagation of a solitary wave and interaction of two solitary waves. For the first test problem, the convergence rate is computed for the proposed algorithms and the L ∞ error norm is used to measure the differences between the exact and numerical solutions. The three conserved quantities of motion are calculated to determine the conservation properties of the two proposed algorithms for both test problems. © 2012 Allerton Press, Inc.