Electron. J. Differential Equations, Vol. 2024 (2024), No. 38, pp. 1-12.

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

Sitong Dong, Xin Zhang, Yuanfeng Jin

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 4, 2024.
Math Subject Classifications: 65M06, 65M12.
Key Words: Rosenau-Burgers equation; nonlinearized difference scheme; conservation law; convergence.
DOI: 10.58997/ejde.2024.38

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Sitong Dong
Department of Mathematics
Yanbian University
Yanji 133002, China
email: 394018165@qq.com
Xin Zhang
Department of Mathematics Science
Harbin Engineering University
Harbin 150000, China
email: zhangxin2022@hrbeu.edu.cn
Yuanfeng Jin
Department of Mathematics
Yanbian University
Yanji 133002, China
email: yfkim@ybu.edu.cn

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