| Abstract: |
| Singular differential equations are essential for modeling complex phenomena in fields such as fluid dynamics, astronomy, biology, and physics. The Emden-Fowler model, Lane-Emden model, and Thomas-Fermi model are prominent singular models with extensive applications in thermodynamics, astrophysics, and atomic physics. These equations are complex due to the presence of singularities, which makes them difficult to solve analytically. As exact solutions are not always achievable, numerical approaches are crucial for estimating solutions to these equations. Developing robust numerical approaches is vital for addressing the issues associated with singularities. This study investigates the development of the Lucas wavelet artificial neural network model and its application in solving singular differential equations. This approach integrates the efficacy of wavelet theory with the flexibility of artificial neural networks. The wavelet method`s capacity to encapsulate both local and global attributes of the solution is beneficial. Moreover, the neural network approach offers some advantages over alternative numerical methods for managing intricate non-linear models with enhanced efficiency. Comparative analyses demonstrate that this methodology yields accurate and consistent results, making it a powerful tool for scientific and technical problems. |
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