A quintic B-spline technique for a system of Lane-Emden equations arising in theoretical physical applications

Osama Ala'yed; Ahmad Qazza; Rania Saadeh; Osama Alkhazaleh; Osama Ala'yed; Ahmad Qazza; Rania Saadeh; Osama Alkhazaleh

doi:10.3934/math.2024225

AIMS Mathematics

2024, Volume 9, Issue 2: 4665-4683. doi: 10.3934/math.2024225

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Research article

A quintic B-spline technique for a system of Lane-Emden equations arising in theoretical physical applications

1.
Department of Mathematics, Jadara University, Irbid 21110, Jordan
2.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
3.
College of Humanities and Sciences, Thomas Jefferson University, East Falls Campus, Philadelphia, PA, USA

Received: 19 November 2023 Revised: 28 December 2023 Accepted: 29 December 2023 Published: 19 January 2024
MSC : 34K34, 34K32

In the present study, we introduce a collocation approach utilizing quintic B-spline functions as bases for solving systems of Lane Emden equations which have various applications in theoretical physics and astrophysics. The method derives a solution for the provided system by converting it into a set of algebraic equations with unknown coefficients, which can be easily solved to determine these coefficients. Examining the convergence theory of the proposed method reveals that it yields a fourth-order convergent approximation. It is confirmed that the outcomes are consistent with the theoretical investigation. Tables and graphs illustrate the proficiency and consistency of the proposed method. Findings validate that the newly employed method is more accurate and effective than other approaches found in the literature. All calculations have been performed using Mathematica software.
- spline,
- B-spline,
- quintic B-spline,
- differential equations,
- Lane-Emden system
Citation: Osama Ala'yed, Ahmad Qazza, Rania Saadeh, Osama Alkhazaleh. A quintic B-spline technique for a system of Lane-Emden equations arising in theoretical physical applications[J]. AIMS Mathematics, 2024, 9(2): 4665-4683. doi: 10.3934/math.2024225

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Abstract

In the present study, we introduce a collocation approach utilizing quintic B-spline functions as bases for solving systems of Lane Emden equations which have various applications in theoretical physics and astrophysics. The method derives a solution for the provided system by converting it into a set of algebraic equations with unknown coefficients, which can be easily solved to determine these coefficients. Examining the convergence theory of the proposed method reveals that it yields a fourth-order convergent approximation. It is confirmed that the outcomes are consistent with the theoretical investigation. Tables and graphs illustrate the proficiency and consistency of the proposed method. Findings validate that the newly employed method is more accurate and effective than other approaches found in the literature. All calculations have been performed using Mathematica software.

References

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