Novel implicit/explicit local conservative schemes for the regularized long-wave equation and convergence analysis

Two implicit and two explicit schemes preserving the local momentum conservation laws exactly on any time–space region are proposed for the regularized long-wave equation. With appropriate boundary conditions, the schemes will be energy- and mass-preserving globally. Combining with the momentum conservation laws, we obtain the priori estimates of the numerical solution and the error estimates in l∞l∞ norm for the proposed implicit schemes. Numerical experiments show the excellent performance of the proposed schemes and the numerical results coincide with the theoretical ones.