RLW方程的高精度加权平均差分格式  

A Weighted Average Difference Scheme with High-Order Accuracy for the RLW Equation

作　　者：付天浩 王晓峰 刘佳垚 付瑶 FU Tian-hao;WANG Xiao-feng;LIU Jia-yao;FU Yao(School of mathematics and statistics,Minnan Normal University,Zhangzhou 363000,Fujian,China;Fujian Key Laboratory of Granular Computing and Applications,Minnan Normal University,Zhangzhou 363000,Fujian,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]闽南师范大学福建省粒计算及其应用重点实验室,福建漳州363000

出　　处：《喀什大学学报》2024年第3期17-22,共6页Journal of Kashi University

基　　金：福建省自然科学基金项目“纳米流体对流换热的高精度数值算法及其应用”(2020J01796)。

摘　　要：对正则长波(RLW)方程建立一种高精度加权平均差分格式,所建格式是三层隐式的,具有二阶时间精度和四阶空间精度,且能够精确地模拟原问题的质量和能量守恒.利用离散能量法证明了所建格式解的存在性、唯一性、收敛性和稳定性.数值实验验证了理论分析的有效性.A weighted average difference scheme with high-order accuracy is proposed for the Regular Long Wave(RLW)equation.The scheme is three-level implicit in time,and has second-order accuracy in time and fourth-order accuracy in space.Also,the scheme can accurately simulate the mass conservation and energy conservation of the original problem.The existence,uniqueness,convergence and stability of the proposed scheme are proved by the discrete energy method.The validity of the theoretical analysis is verified by nu-merical experiments.

关 键 词：RLW方程 加权平均差分格式 守恒性 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]