基于自适应小波神经网络的第二类Fredholm积分方程数值解法  

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

作　　者：姜微 韩惠丽 李风军 JIANG Wei;HAN Huili;LI Fengjun(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,P.R.China)

机构地区：[1]宁夏大学数学统计学院

出　　处：《应用数学和力学》2019年第12期1399-1408,共10页Applied Mathematics and Mechanics

基　　金：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)~~

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.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.

关 键 词：自适应小波神经网络 第二类FREDHOLM积分方程 数值解 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]