| 基于神经网络的常微分方程数值计算方法 |
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| 引用本文： | 徐理英,朱树人. 基于神经网络的常微分方程数值计算方法[J]. 湖南师范大学自然科学学报, 2007, 30(3): 34-37,54 |
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| 作者姓名： | 徐理英 朱树人 |
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| 作者单位： | 长沙理工大学电气与信息工程学院,中国,长沙,410077 |
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| 基金项目： | 国家自然科学基金资助项目(50677014) |
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| 摘 要： | 科学与工程应用中常用微分方程来建模,提出了一种基于余弦基神经网格的计算微分方程的新方法,其基本思想是以神经网络的输出来近似初值问题中的解析解.为保证算法的收敛性,提出并证明了神经网络算法的收敛性定理,为神经网络学习率的选择提供了依据.通过实例证明了该算法的有效性.
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| 关 键 词： | 神经网络 收敛性 常微分方程 初值问题 |
| 文章编号： | 1000-2537（2007）03-0034-04 |
| 修稿时间： | 2007-05-17 |
A Numerical Method for Solving Ordinary Differential Equations by Using Neural Network |
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| XU Li-ying,ZHU Shu-ren. A Numerical Method for Solving Ordinary Differential Equations by Using Neural Network[J]. Journal of Natural Science of Hunan Normal University, 2007, 30(3): 34-37,54 |
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| Authors: | XU Li-ying ZHU Shu-ren |
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| Abstract: | Differential equations are used to model problems in science and engineering,most of these problems require the solution to an initial-value problem.A new method for solving initial-value problems in ordinary differential equations(ODEs) is proposed.The basic idea is to use the out-put of neural network to approx imate to the solution of the initial-value problems in ODEs.The convergence theorem of neural networks algorithm is given and proved.The accurac and efficiency of the proposed method are validated by the simulation examples of initial-value problems in ODEs. |
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| Keywords: | neural network convergence theorem ordinary differential equation initial-value problem |
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