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Engineering with Computers
Erschienen in: Engineering with Computers 2/2024

17.05.2023 | Original Article

A neural network approach for solving nonlinear differential equations of Lane–Emden type

verfasst von: K. Parand, A. A. Aghaei, S. Kiani, T. Ilkhas Zadeh, Z. Khosravi

Erschienen in: Engineering with Computers | Ausgabe 2/2024

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Abstract

In this paper, we propose an Artificial Neural Network (ANN) method for solving some well-known classes of Lane–Emden type equations which are the important nonlinear singular second order differential equations. In this method, we introduced Legendre and Chebyshev blocks as a new efficient neural network architecture based on mathematical properties of Jacobi polynomials to approximate the solution of nonlinear differential equations. The operational matrix in the back-propagation phase is used to calculate the gradient of the cost function according to the network weights, therefor the computations of this architecture are reduced. In order to determine the effect of Legender and Chebyshev blocks, two similar models were built, one using these blocks as activation functions and one without them. Comparing these two models on different examples shows that these blocks significantly increase the accuracy. Also we compared the present work with some well-known approximate results in several examples, revealing that the proposed architecture is effective and accurate.
Vorheriger Artikel Higher-order block-structured hex meshing of tubular structures
Nächster Artikel FluTO: Graded multi-scale topology optimization of large contact area fluid-flow devices using neural networks

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Metadaten
Titel
A neural network approach for solving nonlinear differential equations of Lane–Emden type
verfasst von
K. Parand
A. A. Aghaei
S. Kiani
T. Ilkhas Zadeh
Z. Khosravi
Publikationsdatum
17.05.2023
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 2/2024
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-023-01836-5

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