Single-layer Laguerre neural network model for solving Lane-Emden-Fowler type equations
- Sena Nur Kurmanç
, - Muttalip Özavşar
Abstract
In this study, a single-layer Functional Link Artificial Neural Network model based on Laguerre polynomials is utilized for solving second-order linear and nonlinear equations of Lane-Emden–Fowler type. By using this model, briefly called LgNN, where hidden layers are obtained by Laguerre polynomials, we first extend the input patterns associated with a given set of nonlinear equations of Lane-Emden Fowler type. Then, we modify the network parameters of such a network thanks to an unsupervised error backpropagation algorithm by Adam optimization. Consequently, we compare our results with those obtained by Chebyshev Neural Network (ChNN) and Legendre Neural Network (LeNN) by solving some initial value problems associated with Lane-Emden–Fowler type equations.Keywords
Lane-Emden–Fowler Equation, Single-Layer Functional Link Artificial Neural Network, Laguerre Neural Network, Chebyshev Neural Network, Legendre Neural Network, Adam Optimization