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.

# 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)
• 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.
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沈阳化工大学材料科学与工程学院 沈阳 110142