A New Numerical Solution to the Lane- Emden Equations with Cylindrical and Planar Polytropes Using the Monte Carlo Method | ||
| Sohag Journal of Sciences | ||
| Volume 9, Issue 4, December 2024, Pages 551-571 PDF (2.08 M) | ||
| Document Type: Regular Articles | ||
| DOI: 10.21608/sjsci.2024.283603.1197 | ||
| Authors | ||
| Samah H El- Essawy* 1; Ahmed A. Soliman2; Mohamed I Nouh1; Helal I Abdel- Rahman1; Gamal A Abd- Elmougod3 | ||
| 1Astronomy Department, National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt | ||
| 2Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt | ||
| 3Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, 22511, Egypt | ||
| Abstract | ||
| Lane-Emden equations are important because they explain a star's internal structure, interstellar matter, molecular clouds, and even spiral arms, which can be computed and utilised to forecast different physical properties. The primary goal of this research is to develop a numerical solution for the Lane-Emden (LE) type equations using the Monte Carlo (MC) method. The MC method is increasingly becoming a valuable tool in various scientific fields and has many applications in multiple disciplines. This paper proposes an MC algorithm that can solve two key problems related to LE-type equations: a 1-D problem for a planar polytrope and a 2-D problem for a cylindrical polytrope. To gauge the performance and effectiveness of the numerical solutions generated by the proposed MC algorithm, we compared them with other numerical methods mentioned in previous literature. Our findings indicate that the MC solutions align with Runge-Kutta (RK) solutions and other numerical methods used to solve these problems. | ||
| Keywords | ||
| Lane-Emden equations; polytrope; Monte Carlo method | ||
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