求解RLW-KdV方程的一个高精度平均隐式守恒差分格式  

A high-accuracy average implicit conservative difference scheme for RLW-KdV equation

作　　者：吴明明 刘哲含 李永正 王婷婷 胡劲松 WU Ming-Ming;LIU Zhe-Han;Li Yong-Zheng;WANG Ting-Ting;HU Jin-Song(School of Science,Xihua University,Chengdu 610039,China;School of Science,Civil Aviation Flight University of China,Guanghan 618307,China;School of Big Data and Artificial Intelligence,Chengdu Technological University,Chengdu 611730,China)

机构地区：[1]西华大学理学院,成都610039 [2]中国民用航空飞行学院理学院,广汉618307 [3]成都工业学院大数据与人工智能学院,成都611730

出　　处：《四川大学学报(自然科学版)》2025年第2期340-346,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11701481);四川应用基础研究项目(2019JY0387);中国民用航空飞行学院中央高校基本科研业务费资助项目(PHD2023-047)。

摘　　要：对RLW-KdV方程的初边值问题,本文提出了一个三层高精度平均隐式守恒差分格式.在空间层,差分格式利用Taylor展开进行了部分外推组合处理,以便从整体上抵消截断误差的2阶部分.在时间层,差分格式采用平均隐式格式将问题的非线性项全部控制在已知层.该差分格式在时间和空间方向分别达到2阶和4阶精度,并合理地模拟了原问题的一个守恒量.本文利用离散泛函分析方法和离散Sobolev嵌入不等式给出了差分格式的收敛性和稳定性.数值算例验证了差分格式的有效性.In this paper,a three-level high-accuracy conservative difference scheme is proposed for the initial boundary value problem of RLW-KdV equation.Combining the Taylor expansion with the partial extrapolation in the spatial layer of difference scheme,the second-order term of the truncation error is removed.The averaged implicit scheme is applied in the temporal layer of difference scheme.The difference scheme possesses fourth-order accuracy in the spatial direction and second-order accuracy in the temporal direction and reasonably simulates a conservative property of the original problem.Using the discrete Sobolev embedding inequality and the discrete functional analysis method,the convergence and stability of the difference scheme are given.Numerical examples demonstrate the effectiveness of the difference scheme.

关 键 词：RLW-KdV方程 守恒 收敛性 稳定性 

分 类 号：O241.82[理学—计算数学]