Artificial neural networks for the wavelet analysis of Lane-Emden equations: exploration of astrophysical enigma

The equations of Lane-Emden (LE) can be visualized in various phenomena of astrophysics, fluid mechanics, polymer science and material science, thus the main concern of the present study is to put a novel effort to resolve these equations by utilizing the artificial neural networking approach incorporation with Vieta-Lucas wavelets called as VLW-ANN method. This unique combination of neural networking and Vieta-Lucas wavelets has been prepared to reduce the computational challenges as well as to overcome the obstacles while dealing with singularity. Many examples of the LE variety are solved by this approach. The effectiveness, accuracy and simplicity of the VLW-ANN scheme are demonstrated by a comparative study between the VLW-ANN results and existing results. Additionally, the results are shown in tables and figures, which give a more favorable impression of the scheme's dependability. VLW-ANN scheme will provide interesting results for other non-linear models.