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: 1200
- HTML全文浏览量: 229
- PDF下载量: 350
- 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)

[1]	郭钊, 郭子涛, 易玲艳. 多裂纹问题计算分析的本征COD边界积分方程方法[J]. 应用数学和力学, 2019,40(2): 200-209.(GUO Zhao, GUO Zitao, YI Lingyan. Analysis of multicrack problems with eigen COD boundary integral equations[J]. Applied Mathematics and Mechanics,2019,40(2): 200-209.(in Chinese))
[2]	KIRAN M S. Particle swarm optimization with a new update mechanism[J]. Applied Soft Computing,2017,60: 670-678.
[3]	仪明旭, 陈一鸣, 魏金侠, 等. 应用Haar小波求解非线性分数阶Fredholm积分微分方程[J]. 河北师范大学学报(自然科学版), 2012,36(5): 452-455.(YI Mingxu, CHEN Yiming, WEI Jinxia, et al. Haar wavelet method for solving nonlinear Fredholm integro-differential equations of fractional order[J]. Journal of Hebei Normal University(Natural Science),2012,36(5): 452-455.(in Chinese))
[4]	BIAZAR J, GHAZVINI H. Convergence of the homotopy perturbation method for partial differential equations[J].Nonlinear Analysis: Real World Applications,2009,10(5): 2633-2640.
[5]	DONG Chunhuan, CHEN Zhong, JIANG Wei. A modified homotopy perturbation method for solving the nonliner mixed Volterra-Fredholm inegral equation[J]. Journal of Computational and Applied Mathematics,2013,239: 359-366.
[6]	BRUNNER H. Iterated collocation methods and their discretizations for Volterra integral equations[J]. SIAM Journal on Numerical Analysis,1984,21(6): 1132-1145.
[7]	张志刚, 赵新泉. 利用BP人工神经网络计算Fredholm-Ⅱ型积分方程的近似解[J]. 中南民族大学学报(自然科学版), 2002,21(4): 79-81.(ZHANG Zhigang, ZHAO Xinquan. Solving Fredholm-Ⅱ integral equations by using BP neural network[J]. Journal of South-Central University for Nationalities(Natural Science Edition),2002,21(4): 79-81.(in Chinese))
[8]	王小华, 何怡刚. 三角基函数神经网络算法在数值积分中的应用研究[J]. 电子与信息学报, 2004,26(3): 394-399.(WANG Xiaohua, HE Yigang. Numerical integration study based on triangle basis neural network algorithm[J]. Journal of Electronics & Information Technology,2004,26(3): 394-399.(in Chinese))
[9]	JAFARIAN A, MEASOOMY NIA S. Utilizing feed-back neural network approach for solving linear Fredholm integral equations system[J]. Applied Mathematical Modelling,2013,37(7): 5027-5038.
[10]	闫丽娜, 王珂. 基于神经网络的数值积分改进算法[J]. 应用数学与计算数学学报, 2017,30(4): 520-525.(YAN Lina, WANG Ke. Improved numerical integration algorithm based on neural network[J]. Communication on Applied Mathematics and Computation,2017,30(4): 520-525.(in Chinese))
[11]	刘经纬, 赵辉, 周瑞, 等. 高精度自适应小波神经网络人工智能方法探索[J]. 计算机科学与技术边界学报, 2016,10(8): 1122-1132.(LIU Jingwei, ZHAO Hui, ZHOU Rui, et al. Exploration of high-precision adaptive wavelet neural network artificial intelligence method[J]. Journal of Frontiers of Computer Science and Technology,2016,10(8): 1122-1132.((in Chinese))
[12]	ZHANG Q, BMVENLSTE A. Wavelet networks[J]. IEEE Transactions on Neural Networks,1992,3(6): 889-898.
[13]	黄同成. 基于小波神经网络理论的VOCR与HOCR技术研究[D]. 博士学位论文. 上海: 上海大学, 2008.(HUANG Tongcheng. Research on VOCR and HOCR technology based on wavelet neural network theory[D]. PhD Thesis. Shanghai: Shanghai University, 2008.(in Chinese))
[14]	ALEXANDRIDIS A K, ZAPRANIS A D. Wavelet neural networks: a practical guide[J]. Neural Networks,2013,42:1-27.
[15]	刘经纬, 王普. 基于自适应小波神经网络的复杂系统模式识别方法[J]. 北京工业大学学报, 2014,40(6): 843-850.(LIU Jingwei, WANG Pu. Complex system pattern recognition method based on adaptive wavelet neural network[J]. Journal of Beijing University of Technology,2014,40(6): 843-850.(in Chinese))
[16]	李星. 积分方程[M]. 北京: 科学出版社, 2008.(LI Xin. Integral Equation [M]. Beijing: Science Press, 2008.(in Chinese))

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文章访问数: 1200
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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.