A Weighted Linear Conservative Finite Difference Scheme for Rosenau-Kawahara Equation

In this paper, a linear conservation finite difference scheme with one weighted coefficient is designed by LAX scheme.The scheme has the advantages that it preserves some invariant properties of the original differential equation.It simulated the conservation properties of the problem well.The prior estimate, existence and uniqueness of the finite difference solution were also obtained.It was proved that the finite difference scheme is convergent with second-order and unconditionally stable by energy method.Numerical experiment result shows that appropriate adjustments to the weighted parameters would significantly improve the computational accuracy.