A second order convergent difference scheme for the initial-boundary value problem of Rosenau-Burgers equation

We construct a two-level implicit nonlinear finite difference scheme for the initial boundary value problem of Rosenau-Burgers equation based on the method of order reduction. We discuss conservation, unique solvability, and convergence for the difference scheme. The new scheme is shown to be second-order convergent in time and space. Finally, numerical simulations illustrate our theoretical analysis. For more information see https://ejde.math.txstate.edu/Volumes/2024/38/abstr.html