| Lax等价定理在非线性方面的推广 |
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| 引用本文： | 胡庆云. Lax等价定理在非线性方面的推广[J]. 应用数学, 2002, 15(1): 62-67 |
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| 作者姓名： | 胡庆云 |
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| 作者单位： | 南京河海大学理学院,江苏,南京,210000 |
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| 摘 要： | 本文证明了，用差分法求解非线性发展方程的初值问题，当方程适定，在差分格式相容的条件下，稳定性等价于收敛性和逐点Lipschitz条件。从而推广了对线性发展方程成立的Lax等价定理。
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| 关 键 词： | 非线性发展方程 初值问题 差分法 Lax等价定理 稳定性 收敛性 差分格式 |
| 文章编号： | 1001-9847(2002)01-0062-06 |
| 修稿时间： | 2001-08-18 |
An Extension of Lax Theorem to the Nonlinear Case |
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| HU Qing-yun. An Extension of Lax Theorem to the Nonlinear Case[J]. Mathematica Applicata, 2002, 15(1): 62-67 |
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| Authors: | HU Qing-yun |
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| Abstract: | The evolution equation is a system of partial difference eq ua tions, which has been widely applied in the dynamic mechanics theory and enginee ring. The difference method is adopted to solve the initial value problem of the nonlinear evolution equation in this paper. The solution stability is proved to be equivalent to the convergency and the point-by-point Lipschitz condition i f the equation is well posed and the difference pattern is compatible. As a resu lt, this leads to an extension of Lax theorem to the nonlinear case. |
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| Keywords: | Initial value problem of the nonlinear evolution equation D ifference method Lax theorem Stability Convergency Point-by-point Lipschit z condition |
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