A discrete Hahn wavelet neural network method for Bratu-type equations

Authors
Parisa Rahimkhani 1
Yadollah Ordokhani 2
1 Mahallat Institute of Higher Education
2 Alzahra University
Abstract
In this paper, a new numerical method based on the neural network and the discrete Hahn wavelets is presented for solving the Bratu-type equations. First, the discrete Hahn wavelets and some of their important properties are expressed to construct the Hahn wavelets neural network. The presented neural network consists of three layers: input layer, hidden layer, output layer. In this method, the Hahn wavelets and sinh functions are used as the activation functions of the hidden layer and output layer, respectively. Then, an analytical optimization method is employed to adjust the neural network weights so that the approximated solution satisfies the given problem. Using this method, the original problem is converted into a system of algebraic equations, which is solved by Newton’s iterative method. Finally, the accuracy and efficiency of the proposed method are examined through several numerical examples.
Keywords
Neural Network
Hahn wavelets
Bratu equations
Numerical method
Analytical optimization method
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