Asymptotic analysis and error estimate for Rosenau-Burgers equation (Q2299022)

Summary: 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 \(\mathcal{O}(\Delta t^2 + N^{2 - m})\), 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.