JIANG Wei, HAN Huili, LI Fengjun. Numerical Solution to the Second Kind of Fredholm Integral Equation Based on the Adaptive Wavelet Neural Network[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1399-1408. doi: 10.21656/1000-0887.400029
Citation: JIANG Wei, HAN Huili, LI Fengjun. Numerical Solution to the Second Kind of Fredholm Integral Equation Based on the Adaptive Wavelet Neural Network[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1399-1408. doi: 10.21656/1000-0887.400029

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

doi: 10.21656/1000-0887.400029
Funds:  The National Natural Science Foundation of China(61662060;11762016)
  • Received Date: 2019-01-10
  • Rev Recd Date: 2019-10-30
  • Publish Date: 2019-12-01
  • 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.
  • loading
  • [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))
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (925) PDF downloads(344) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return