Asymptotic Analysis and Error Estimate for Rosenau-Burgers Equation

In this work, the asymptotic stability result for Rosenau-Burgers equation is established, under appropriate assumptions on steady state eigenvalue problem and the forcing function. In addition, we propose and analyze a linearized numerical method for solving this nonlinear Rosenau-Burgers equation. We prove that the numerical scheme is unconditionally stable, and the error estimate shows that the numerical method is in the order of O(Delta t2+N2-m), where Delta t, N, and m are, respectively, step of time, polynomial degree, and regularity of u. Numerical examples are illustrated to verify the theoretical results.