二维非线性RLW方程的守恒差分格式  

A Conservative Finite Difference Scheme for 2D Nonlinear RLW Equation

作　　者：蒋菊霞 王波[2] 王晓峰 JIANG Ju-xia1, WANG Bo2, WANG Xiao-feng3(1. School of Mathematics and Information Science, Xinxiang University, Xinxiang 453003, China） （2. Office of Admission and Employment, Sanmenxia Polytechnic College, Sanmenxia 472000, China） （3. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China)

机构地区：[1]新乡学院数学与信息科学学院,河南新乡453003 [2]三门峡职业技术学院招生与就业处,河南三门峡472000 [3]河南科技学院数学科学学院,河南新乡453003

出　　处：《数学的实践与认识》2018年第17期229-237,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(U1304106);河南科技学院重大培育项目(2016ZD010)

摘　　要：对二维非线性正则长波（RLW）方程初边值问题的数值解法进行了研究,提出了一个三层守恒差分格式.证明了差分解的存在唯一性,并利用能量方法分析了该格式的二阶收敛性与无条件稳定性.数值算例验证了格式的可靠性,且运算过程中保持了能量守恒.A three-level conservative finite difference scheme for solving the initial boundary value problem of 2D nonlinear regular long wave （RLW） is proposed. The existence, uniqueness, and conservation for energy of the scheme are proved by discrete energy method. The new scheme is 2nd-order convergent and unconditionally stable. Numerical examples verify that the scheme is efficient and reliable.

关 键 词：RLW方程 守恒格式 离散能量法 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]