| Rosenau-KdV方程的一个双加权线性守恒差分格式 |
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| 引用本文： | 陈涛,胡劲松. Rosenau-KdV方程的一个双加权线性守恒差分格式[J]. 西华大学学报(自然科学版), 2016, 35(2): 88-93, 103. DOI: 10.3969/j.issn.1673-159X.2016.02.017 |
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| 作者姓名： | 陈涛 胡劲松 |
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| 作者单位： | 西华大学理学院，四川 成都 610039 |
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| 基金项目： | 西华大学重点基金项目z1513324 |
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| 摘 要： | 对Rosenau-KdV方程的初边值问题进行数值研究，提出一个带有2个加权系数的三层线性守恒差分格式对原问题的2个守恒性质进行模拟，得到差分解的先验估计和存在唯一性；利用离散泛函分析方法分析了差分格式的二阶收敛性与无条件稳定性。数值实验表明，该方法是可行的，且适当调整2个加权系数可以显著提高计算精度。
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| 关 键 词： | Rosenau-KdV方程 守恒差分格式 加权 收敛性 稳定性 |
| 收稿时间： | 2014-10-17 |
A Double Weighted Linear Conservative Difference Scheme for Rosenau-KdV Equation |
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| CHEN Tao,HU Jinsong. A Double Weighted Linear Conservative Difference Scheme for Rosenau-KdV Equation[J]. Journal of Xihua University(Natural Science Edition), 2016, 35(2): 88-93, 103. DOI: 10.3969/j.issn.1673-159X.2016.02.017 |
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| Authors: | CHEN Tao HU Jinsong |
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| Affiliation: | School of Science, Xihua University, Chengdu 610039 China |
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| Abstract: | The numerical solution for an initial boundary value problem of Rosenau - KdV equation is considered. A linear three-level conservation finite difference scheme with two weighted coefficient is designed. The finite difference scheme simulates the conservation properties of the problem well. The prior estimate, existence and uniqueness of the finite difference solution are also obtained. It is proved that the finite difference scheme is convergent with second-order and unconditionally stable with discrete functional analysis method. Numerical experiment result also shows that appropriate adjustments to the two weighted parameters would significantly improve the computational accuracy. |
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