四川大学学报（自然科学版）2025，Vol.62Issue(2)：340-346,7.DOI:10.19907/j.0490-6756.240166
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
摘要
Abstract
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 extrapola-tion 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 pos-sesses 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Key words
RLW-KdV equation/Conservation/Convergence/Stability(2020 MSC 65M06)分类
数理科学引用本文复制引用
吴明明,刘哲含,李永正,王婷婷,胡劲松..求解RLW-KdV方程的一个高精度平均隐式守恒差分格式[J].四川大学学报（自然科学版）,2025,62(2):340-346,7.基金项目
国家自然科学基金(11701481) （11701481）
四川应用基础研究项目(2019JY0387) （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) （PHD2023-047）
