Numerical solution of coupled system of  Emden-Fowler equations using artificial neural network technique

Ashish  Kumar; Manoj Kumar; Pranay  Goswami

doi:10.11121/ijocta.1424

Authors

Ashish Kumar School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, Delhi, India https://orcid.org/0009-0003-8968-8074
Manoj Kumar Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi, India https://orcid.org/0000-0001-8218-8278
Pranay Goswami School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, Delhi, India https://orcid.org/0000-0003-1205-1975

DOI:

https://doi.org/10.11121/ijocta.1424

Keywords:

Coupled system of Emden-Fowler equations, Numerical method, Deep neural network technique

Abstract

In this paper, a deep artificial neural network technique is proposed to solve the coupled system of Emden-Fowler equations. A vectorized form of algorithm is developed. Implementation and simulation of this technique is performed using Python code. This technique is implemented in various numerical examples, and simulations are conducted. We have shown graphically how accurately this method works. We have shown the comparison of numerical solution and exact solution using error tables. We have also conducted a comparative analysis of our solution with alternative methods, including the Bernstein collocation method and the Homotopy analysis method. The comparative results are presented in error tables. The efficiency and accuracy of this method are demonstrated by these graphs and tables.

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Author Biographies

Ashish Kumar, School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, Delhi, India

Ashish Kumar received graduation degree in mathematics (Honours) from Ramjas College, University of Delhi, and Msc degree from Hindu College, University of Delhi. Currently, he is a junior research fellow at School of Liberal Studies, Dr. B.R. Ambedkar University Delhi, Delhi. His research interests include numerical analysis and applied mathematics.

Manoj Kumar, Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi, India

Manoj Kumar is a visiting faculty member at the Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi, India. He received a PhD degree in Mathematics from Dr. B. R. Ambedkar University Delhi, India. His research interests include traffic congestion modeling, machine learning, and deep learning.

Pranay Goswami, School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, Delhi, India

Pranay Goswami is currently an Assistant Professor at the School of Liberal Studies, Dr. B.R. Ambedkar University Delhi. He received PhD degree in Mathematics from University of Rajasthan, India. His research interests include differential equations, fractional differential equations, numerical methods, and mathematical modeling.

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