Volume 12, Issue 1 (6-2026)
mmr 2026, 12(1): 92-109 |
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Rahimkhani P, Ordokhani Y. A discrete Hahn wavelet neural network method for Bratu-type equations. mmr 2026; 12 (1) :92-109
URL: http://mmr.khu.ac.ir/article-1-3431-en.html
URL: http://mmr.khu.ac.ir/article-1-3431-en.html
1- Mahallat Institute of Higher Education
2- Alzahra University ,ordokhani@alzahra.ac.ir
2- Alzahra University ,
Abstract: (58 Views)
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
Type of Study: S |
Subject:
Mat
Received: 2024/11/22 | Revised: 2026/06/12 | Accepted: 2026/04/15 | Published: 2026/06/12 | ePublished: 2026/06/12
Received: 2024/11/22 | Revised: 2026/06/12 | Accepted: 2026/04/15 | Published: 2026/06/12 | ePublished: 2026/06/12
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