A conservative fourth-order stable finite difference scheme for the generalized Rosenau-KdV equation in both 1D and 2D

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:355

Article

Wang, Xiaofeng^1,2  Dai, Weizhong³ 

[1] Minnan Normal Univ, Sch Math & Stat, Zhangzhou 363000, Fujian, Peoples R China

[2] Henan Inst Sci & Technol, Sch Math Sci, Xinxiang 453003, Henan, Peoples R China

[3] Louisiana Tech Univ, Coll Engn & Sci, Math & Stat, Ruston, LA 71272 USA

关键词: Rosenau-KdV equation;    Conservative scheme;    Discrete energy method;    Unconditional stability;   

DOI  :  10.1016/j.cam.2019.01.041

来源: Elsevier

【 摘 要 】

In the present work, a conservative fourth-order stable finite difference scheme is proposed to solve the generalized Rosenau-KdV equation in both 1D and 2D. The existence, uniqueness, and mass and energy conservations of the numerical solution are proved using the discrete energy method. The new scheme is convergent with O(tau(2)+h(4)) and unconditionally stable. Numerical experiments are carried out to show that the scheme is efficient and reliable. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free