Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique
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 numerica...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Balikesir University
2024-01-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
| Subjects: | |
| Online Access: | http://ijocta.org/index.php/files/article/view/1424 |
| _version_ | 1797360281026822144 |
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| author | Ashish Kumar Manoj Kumar Pranay Goswami |
| author_facet | Ashish Kumar Manoj Kumar Pranay Goswami |
| author_sort | Ashish Kumar |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-03-08T15:36:05Z |
| format | Article |
| id | doaj.art-f2ea009ad05c4b62bf65af3572f24a09 |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-03-08T15:36:05Z |
| publishDate | 2024-01-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-f2ea009ad05c4b62bf65af3572f24a092024-01-09T23:35:49ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032024-01-0114110.11121/ijocta.1424Numerical solution of coupled system of Emden-Fowler equations using artificial neural network techniqueAshish Kumar0Manoj Kumar1Pranay Goswami2School of Liberal Studies, Dr. B. R. Ambedkar University Delhi, Delhi, IndiaDepartment of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi, IndiaSchool of Liberal Studies, Dr. B. R. Ambedkar University Delhi, Delhi, India 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. http://ijocta.org/index.php/files/article/view/1424Coupled system of Emden-Fowler equationsNumerical methodDeep neural network technique |
| spellingShingle | Ashish Kumar Manoj Kumar Pranay Goswami Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique An International Journal of Optimization and Control: Theories & Applications Coupled system of Emden-Fowler equations Numerical method Deep neural network technique |
| title | Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique |
| title_full | Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique |
| title_fullStr | Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique |
| title_full_unstemmed | Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique |
| title_short | Numerical solution of coupled system of Emden-Fowler equations using artificial neural network technique |
| title_sort | numerical solution of coupled system of emden fowler equations using artificial neural network technique |
| topic | Coupled system of Emden-Fowler equations Numerical method Deep neural network technique |
| url | http://ijocta.org/index.php/files/article/view/1424 |
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