A Nonlinear Weighted Conserved Difference Scheme for the Generalized Rosenau-Kawahara Equation

A numerical method for a class of generalized Rosenau-Kawahara equation with initial boundary value problem is studied. Based on the second order accuracy, a nonlinear two-level difference scheme is constructed when two weighted coefficients are introduced at the space level. The scheme can reasonably simulate the original conservation. By the discrete functional analysis method, the second order convergence and stability of the scheme are analyzed. Numerical experiments results show that the calculation accuracy can be greatly improved by adjusting the two weighting coefficients, which proves that the weighting scheme proposed in this paper is effective.