| 一个解KdV方程的满足两个守恒律的差分格式 |
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| 引用本文： | 崔艳芬,茅德康.一个解KdV方程的满足两个守恒律的差分格式[J].应用数学与计算数学学报,2005,19(2):15-22. |
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| 作者姓名： | 崔艳芬 茅德康 |
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| 作者单位： | 上海大学数学系,上海,200444 |
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| 摘 要： | Korteweg-de Vries(KdV)方程是人们在研究一些物理问题时得到的非线性波 动方程,其解满足无穷多个守恒律．本文为该方程设计了一种差分格式,其采用的是有限 体积法．但与传统的有限体积法不同的是,它的数值解同时满足两个相关的守恒律．这样 可以更好地保持解的物理上的守恒性质．数值例子表明这一算法是有效的．
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| 关 键 词： | KdV方程 守恒律 网格平均 函数重构 |
| 收稿时间： | 2005-04-08 |
| 修稿时间： | 2005年4月8日 |
A Difference Scheme Satisfying Two Conservation Laws for KdV Equation |
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| Cui Yanfen,Mao Dekang.A Difference Scheme Satisfying Two Conservation Laws for KdV Equation[J].Communication on Applied Mathematics and Computation,2005,19(2):15-22. |
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| Authors: | Cui Yanfen Mao Dekang |
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| Abstract: | Korteweg-de Vries(KdV) equation is a nonlinear wave equation arising from physics study, whose solution satisfies infinitely many conservation laws. This paper designs a difference scheme for the equation, which is of the finite-volume type. Different from the traditional finite-volume schemes however, the scheme satisfies two related conservation laws of the equation. Designed in such a way, the scheme preserves better the physical conservation properties of the KdV equation. The numerical examples show the efficiency of the scheme. |
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| Keywords: | KdV equation conservation laws cell-average reconstruction |
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