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Numerical solution for non-linear differential equation of Emden-Fowler by artificial neural network | ||
| Journal of University of Anbar for Pure Science | ||
| Volume 20, Issue 2, August 2026, Pages 404-412 PDF (599.81 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2026.166401.1789 | ||
| Author | ||
| Nahid Salim Mohammed Al-Saif* | ||
| Department of Mathematics, College of Science, University of Anbar, Iraq | ||
| Abstract | ||
| The Emden − Fowler equation (𝐸 − 𝐹 − Eq) is used in math and other sciences lik chemistry, astrophysics and physics. It can also be changed to become the Lane- Emden equation (L_E_Ed) by using a specific function, and it is applied in various scientific fields along with math. Many researchers examine different ways, both analytical and numerical, to solve these types of equations, whether they are linear or nonlinear. Using artificial intelligence and machine learning, we can now find solution to complicated equations more quickly and accurately than with traditional methods. The goal of this study is solution (𝐸 − 𝐹 − Eq) singular second order differential equations via neural network by three main steps. First, a neural network (A-N-N) setup (a type of algorithm) is created to mimic the problem being worked on. Next, this algorithm is used to find a numerical solution for (𝐸 − 𝐹 − Eq). Finally, the results are compared with well-known approximate answers from various examples, using tables and figures for specific parameters to show the accuracy and effectiveness of the ANN method. | ||
| Keywords | ||
| Artificial Neural Networks (A-N-N); Emden-Fowler equation (𝐸 − 𝐹 − Eq); LM Training; Tansig (tanh) function | ||
| References | ||
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