Local momentum-preserving algorithms for the GRLW equation

In this paper, four local momentum-preserving (LMP) algorithms for the GRLW equation are studied. The proposed algorithms, which conserve the local momentum conservation in any local time-space region, are proved to be momentum- and mass-preserving globally with appropriate boundary conditions. Two of the algorithms are explicit, and the other two are implicit. We make nonlinear convergence and stability analysis for the implicit algorithms. Numerical experiments confirm the long time preservation of the proposed algorithms and verify the theoretical analysis.