Rosenau-RLW方程的拟紧致C-N守恒差分格式  

Pseudo-compact Crank-Nicolson conservative difference scheme for Rosenau-RLW Equations

作　　者：傅雨泽 胡兵[1] 郑茂波[2] 

机构地区：[1]四川大学数学学院,成都610064 [2]成都工业学院,成都611730

出　　处：《四川大学学报（自然科学版）》2014年第6期1143-1148,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金项目(11271273)

摘　　要：本文对Rosenau-RLW方程的初边值问题进行了数值研究,提出了一个隐式拟紧致C-N差分格式,该格式很好地模拟了问题的守恒性质.通过Brouwer不动点定理,本文得到了差分解的存在性,给出了解的先验估计和误差估计,并通过离散能量法分析了该格式的稳定性、二阶收敛性和解的唯一性.数值算例表明,该格式是可行的,且相对于一般的二层格式具有更好的计算精度.In this paper, a numerical method for an initial-boundary value problem of the Rosenau-RLW equation is considered. An implicit pseudo-compact Crank-Nicolson finite difference is proposed. This scheme simulates the conservation properties of the problem quite well. Then, existence of the numeri- cal solutions is derived by Brouwer fixed point theorem. A priori bound and the error estimates are dis- cussed. Finally, stability, second-order convergence and uniqueness of the scheme are proved in terms of the discrete energy method. Numerical examples show that this scheme is feasible and its accuracy is better than the known difference schemes.

关 键 词：Rosenau-RLW方程 C-N守恒格式 存在性 收敛性 稳定性 唯一性 

分 类 号：O241.82[理学—计算数学]