A high-precision implicit nonlinear conservation numerical scheme for Rosenau-Burgers equation by multiple varying bound integral method

Abstract This paper mainly focuses on the numerical study of fourth-order nonlinear Rosenau-Burgers equation. Firstly, the intermediate variables are introduced to reduce the orders of original differential equation. Secondly, we combine the Multiple Varying Bound Integral (MVBI) Method, which is a way for us to eliminate the derivatives in original differential equation, with Taylor Function Fitted (TFF) method to construct nonlinear implicit discrete scheme with four-order precision in space direction and two-order precision in time direction, for Rosenau-Burgers equation. At the same time, we prove that this numerical scheme is consistent with original equation in the energy property. In addition, the well-posedness of this numerical solution and convergence are both proved. Finally, numerical experiments are carried out to verify the effectiveness of this numerical scheme.