| Rosenau-KdV方程初边值问题的一个高精度线性守恒差分格式 |
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| 引用本文： | 李贵川,张芝源,胡劲松,章浩洲.Rosenau-KdV方程初边值问题的一个高精度线性守恒差分格式[J].四川大学学报(自然科学版),2022,59(2):021005-021005-8. |
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| 作者姓名： | 李贵川 张芝源 胡劲松 章浩洲 |
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| 作者单位： | 西华大学土木建筑与环境学院,西华大学理学院,西华大学理学院,四川大学数学学院 |
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| 基金项目： | 四川省应用基础研究项目(2019YJ0387) |
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| 摘 要： | 本文针对Rosenau-KdV方程的初边值问题提出了一个高精度三层线性差分格式，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及先验误差估计，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.
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| 关 键 词： | Rosenau-KdV方程 差分格式 守恒律 收敛性 稳定性 |
| 收稿时间： | 2021/10/8 0:00:00 |
| 修稿时间： | 2021/12/1 0:00:00 |
A high-accuracy linear conserative difference scheme for the initial-boundary value problem of Rosenau-KdV equation |
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| LI Gui-Chuan,ZHANG Zhi-Yuan,HU Jin-song and ZHANG Hao-Zhou.A high-accuracy linear conserative difference scheme for the initial-boundary value problem of Rosenau-KdV equation[J].Journal of Sichuan University (Natural Science Edition),2022,59(2):021005-021005-8. |
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| Authors: | LI Gui-Chuan ZHANG Zhi-Yuan HU Jin-song and ZHANG Hao-Zhou |
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| Institution: | School of Architecture and Civil Engineering, Xihua University,School of Science, Xihua University,School of Science, Xihua University,School of Science, Sichuan University |
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| Abstract: | In this paper, a three-level linear finite difference scheme with high theoretical accuracy is proposed for the initial-boundary value problem of Rosenau-KdV equation. This scheme simulates two conservative properties very well. The existence and 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. |
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| Keywords: | Rosenau-KdV equation Difference scheme Conservative law Convergence Stability |
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