Rosenau-KdV方程初边值问题的一个高精度线性守恒差分格式  

A high-accuracy linear conservative difference scheme for the initial-boundary value problem of Rosenau-KdV equation

作　　者：李贵川 张芝源 胡劲松 章皓洲 LI Gui-Chuan;ZHANG Zhi-Yuan;HU Jin-Song;ZHANG Hao-Zhou(School of Architecture and Civil Engineering,Xihua University,Chengdu 610039,China;School of Science,Xihua University,Chengdu 610039,China;School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]西华大学土木建筑与环境学院,成都610039 [2]西华大学理学院,成都610039 [3]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2022年第2期25-32,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省应用基础研究项目(2019YJ0387)。

摘　　要：本文针对Rosenau-KdV方程的初边值问题提出了一个具有O(τ^(2)+h^(4))精度的三层线性差分格式,该格式能够较好地保持两个守恒不变量.此外,本文还得到了差分解的存在唯一性和先验误差估计,并通过能量方法证明了数值格式的收敛性和稳定性.数值算例验证了理论结果.In this paper, a three-level linear finite difference scheme with theoretical accuracy of O(τ^(2)+h^(4)) is proposed for the initial-boundary value problem of Rosenau-KdV equation. This scheme simulates two conservative properties very well. The existence, uniqueness of the difference solution and prior estimates are obtained. Then the convergence and stability of the scheme are analyzed by using the energy method. Numerical examples verify the theoretical results.

关 键 词：KDV方程 初边值问题 解的存在唯一性 先验误差估计 能量方法 数值格式 线性差分格式 守恒差分格式 

分 类 号：O175.26[理学—数学]