基于自适应小波神经网络的第二类Fredholm积分方程数值解法

姜微; 韩惠丽; 李风军

doi:10.21656/1000-0887.400029

基于自适应小波神经网络的第二类Fredholm积分方程数值解法

doi: 10.21656/1000-0887.400029

宁夏大学数学统计学院, 银川 750021

基金项目: 国家自然科学基金(61662060；11762016)；宁夏自然科学基金(2019AAC03037);宁夏高等学校自然科学研究项目(NGY2017018)

详细信息

作者简介:
姜微(1994—), 女, 硕士生(E-mail: 281192409@qq.com);韩惠丽(1972—), 女, 教授, 博士(通讯作者. E-mail: nxhan@126.com);李风军(1973—), 男, 教授, 博士.

中图分类号: TP183
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- 文章访问数: 1199
- HTML全文浏览量: 228
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- 被引次数: 0
出版历程
- 收稿日期: 2019-01-10
- 修回日期: 2019-10-30
- 刊出日期: 2019-12-01

Numerical Solution to the Second Kind of Fredholm Integral Equation Based on the Adaptive Wavelet Neural Network

School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China

Funds: The National Natural Science Foundation of China(61662060；11762016)

摘要

摘要: 该文构造了一类三层前馈自适应小波神经网络,将小波分析中平移因子和伸缩因子的拟合设置为输入层到隐层的权值与阈值,采用小波基函数作为隐层激活函数,并根据梯度下降算法自适应地调整参数.应用自适应小波神经网络数值求解第二类Fredholm积分方程,通过数值算例验证了该方法的可行性和有效性.
- 自适应小波神经网络 /
- 第二类Fredholm积分方程 /
- 数值解
Abstract: A 3-layer feedforward adaptive wavelet neural network model was constructed. The fitting of the translation factor and the scaling factor were combined in the wavelet analysis. The result of combination was set as the weight and bias of the hidden layer. The wavelet basis function was used as the hidden layer activation function and the parameters could be adaptively adjusted according to the gradient descent algorithm. Numerical solution to the second kind of Fredholm integral equation was solved with the adaptive wavelet neural network, and the feasibility and validity of the method were verified through numerical examples.
- adaptive wavelet neural network /
- second kind of Fredholm integral equation /
- numerical solution

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参考文献(16)

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文章访问数: 1199
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基于自适应小波神经网络的第二类Fredholm积分方程数值解法

doi: 10.21656/1000-0887.400029

作者简介:
姜微(1994—), 女, 硕士生(E-mail: 281192409@qq.com);韩惠丽(1972—), 女, 教授, 博士(通讯作者. E-mail: nxhan@126.com);李风军(1973—), 男, 教授, 博士.

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Numerical Solution to the Second Kind of Fredholm Integral Equation Based on the Adaptive Wavelet Neural Network

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基于自适应小波神经网络的第二类Fredholm积分方程数值解法

doi: 10.21656/1000-0887.400029

作者简介: 姜微(1994—), 女, 硕士生(E-mail: 281192409@qq.com);韩惠丽(1972—), 女, 教授, 博士(通讯作者. E-mail: nxhan@126.com);李风军(1973—), 男, 教授, 博士.

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出版历程

Numerical Solution to the Second Kind of Fredholm Integral Equation Based on the Adaptive Wavelet Neural Network

计量

出版历程

目录

作者简介:
姜微(1994—), 女, 硕士生(E-mail: 281192409@qq.com);韩惠丽(1972—), 女, 教授, 博士(通讯作者. E-mail: nxhan@126.com);李风军(1973—), 男, 教授, 博士.