Double reduction order method based conservative compact schemes for the Rosenau equation

In this paper, fourth-order compact difference schemes are derived, analyzed and tested at length for both one-and two-dimensional Rosenau equations under the spatial periodic boundary conditions on the basis of the double reduction order method and bilinear compact operator. We prove that these schemes satisfy mass and energy conservation law via the help of the energy method. In addition, the uniquely solvable, unconditional convergence and stability are all obtained with the convergence order four in space and order two in time under the D infinity-norm. Several numerical examples are presented to support the theoretical results.