Monte Carlo simulation of Lane–Emden type equations arising in astrophysics

Monte Carlo (MC) method played an essential role in many areas of human activity and has found application in many branches of physical science. This paper proposes a computational technique based on MC algorithms to solve Lane–Emden (LE) type equations. We analyze four LE equations arising in astro...

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Bibliographic Details
Published in:Astronomy and computing 2023-01, Vol.42, p.100665, Article 100665
Main Authors: El-Essawy, S.H., Nouh, M.I., Soliman, A.A., Abdel Rahman, H.I., Abd-Elmougod, G.A.
Format: Article
Language:English
Subjects:
Lane–Emden equations
Monte Carlo algorithms
Polytropic and isothermal gas spheres
White dwarf equation
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Summary:Monte Carlo (MC) method played an essential role in many areas of human activity and has found application in many branches of physical science. This paper proposes a computational technique based on MC algorithms to solve Lane–Emden (LE) type equations. We analyze four LE equations arising in astrophysics: the positive and negative indices of the polytropic gas spheres, the isothermal gas sphere, and the white dwarf equation. We calculated eleven models (i.e., eleven LE equations) of the positive index polytropes, nine for the negative index polytrope, the isothermal gas sphere, and the white dwarf equation. Comparing the MC and numerical/analytical models gives good agreement for the four LE equations under study.
ISSN:2213-1337
2213-1345
DOI:10.1016/j.ascom.2022.100665