  In this paper, based on the weak form of the Hamiltonian formulation of the
regularized long-wave equation and a novel approach of transforming the
original Hamiltonian energy into a quadratic functional, a fully implicit and
three linear-implicit energy conservation numerical schemes are respectively
proposed. The resulting numerical schemes are proved theoretically to satisfy
the energy conservation law in the discrete level. Moreover, these
linear-implicit schemes are efficient in practical computation because only a
linear system need to be solved at each time step. The proposed schemes are
both second order accurate in time and space. Numerical experiments are
presented to show all the proposed schemes have satisfactory performance in
providing accurate solution and the remarkable energy-preserving property.
