| 数学规划加权残值法在非线性微分方程中的应用 |
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| 引用本文： | 侯宇,沈力行.数学规划加权残值法在非线性微分方程中的应用[J].上海力学,1999,20(3):291-296. |
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| 作者姓名： | 侯宇 沈力行 |
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| 作者单位： | [1]中国计量学院 [2]上海大学 |
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| 基金项目： | 国家教委固体力学开放研究实验室资助 |
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| 摘 要： | 本文研究数学规划加权残值法在非线性微分方程求解中的应用，利用数学规划加权残值法和ＬＰ模理论，把非线性微分方程边值问题转化为一个可微分的无约束非线性优化问题，从而运用成熟稳定的寻优方法求得问题的解。文中数字计算例子表明本文方法可以快速有效地求解非线性微分方程。
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| 关 键 词： | 非线性 微分方程中 数学规划 加权残值法 |
APPLICATION OF METHOD OF WEIGHTED RESIDUAL OF MATHEMATICAL PROGRAMMING ON SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS |
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| Hou Yu Shen Lixing He Fubao.APPLICATION OF METHOD OF WEIGHTED RESIDUAL OF MATHEMATICAL PROGRAMMING ON SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS[J].Chinese Quarterly Mechanics,1999,20(3):291-296. |
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| Authors: | Hou Yu Shen Lixing He Fubao |
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| Abstract: | This paper studies the application of MWR of mathematical programming on the solutions of nonlinear differential equations. By using MWR of mathematical programming and Lp model theory, the boundary-value problem of nonlinear differential equations is expressed as a differentiable and unconstrained nonlinear optimization. And it is easily solved by more optimizing methods. The numerical results of an example in this paper show that the method is effective and fast in the solutions of nonlinear differential equations. |
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| Keywords: | nonlinear differential equations mathematical programming method of weighted residual |
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