Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 38, pp. 1-12.

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

Authors: Sitong Dong (Yanbian Univ., Yanji, China)
         Xin Zhang (Harbin Engineering Univ., Harbin, China}
         Yuanfeng Jin (Yanbian Univ., Yanji, China)

Abstract: 
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.

Submitted December 2, 2023. Published July 04, 2024.
Math Subject Classifications: 65M06, 65M12.
Key Words: Rosenau-Burgers equation; nonlinearized difference scheme; conservation law; convergence.