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386944

A New Numerical Solution to the Lane- Emden Equations with Cylindrical and Planar Polytropes Using the Monte Carlo Method

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Last updated: 29 Dec 2024

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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.

DOI

10.21608/sjsci.2024.283603.1197

Keywords

Lane-Emden equations, polytrope, Monte Carlo method

Authors

First Name

Samah

Last Name

El- Essawy

MiddleName

H

Affiliation

Astronomy Department, National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt

Email

samahessawy1122@gmail.com

City

Cairo

Orcid

0000-0002-3057-0114

First Name

Ahmed

Last Name

Soliman

MiddleName

A.

Affiliation

Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

Email

a_a_sol@hotmail.com

City

Sohag, Egypt

Orcid

-

First Name

Mohamed

Last Name

Nouh

MiddleName

I

Affiliation

Astronomy Department, National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt

Email

abdo_nouh@hotmail.com

City

Cairo

Orcid

0000-0002-8037-6328

First Name

Helal

Last Name

Abdel- Rahman

MiddleName

I

Affiliation

Astronomy Department, National Research Institute of Astronomy and Geophysics, 11421 Helwan, Cairo, Egypt

Email

helal_ismaeil@yahoo.com

City

Cairo

Orcid

-

First Name

Gamal

Last Name

Abd- Elmougod

MiddleName

A

Affiliation

Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, 22511, Egypt

Email

gam_amin@yahoo.com

City

Damanhour

Orcid

-

Volume

9

Article Issue

4

Related Issue

46686

Issue Date

2024-12-01

Receive Date

2024-04-19

Publish Date

2024-12-01

Page Start

551

Page End

571

Print ISSN

2357-0938

Online ISSN

2974-4296

Article File

SJSCI_Volume 9_Issue 4_Pages 551-571.pdf

PDF . 2.2MB

Link

https://sjsci.journals.ekb.eg/article_386944.html

Detail API

https://sjsci.journals.ekb.eg/service?article_code=386944

Order

386,944

Type

Regular Articles

Type Code

2,359

Publication Type

Journal

Publication Title

Sohag Journal of Sciences

Publication Link

https://sjsci.journals.ekb.eg/

MainTitle

A New Numerical Solution to the Lane- Emden Equations with Cylindrical and Planar Polytropes Using the Monte Carlo Method

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Type

Article

Created At

29 Dec 2024