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

JIANG Wei; HAN Huili; LI Fengjun

doi:10.21656/1000-0887.400029

Volume 40 Issue 12

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Article Navigation > Applied Mathematics and Mechanics > 2019 > 40(12): 1399-1408

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

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

doi: 10.21656/1000-0887.400029

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

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

Abstract

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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References(16)

References

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