Numerical solution for the system of Lane-Emden type equations using cubic B-spline method arising in engineering

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

doi:10.3934/math.2023754

AIMS Mathematics

2023, Volume 8, Issue 6: 14747-14766. doi: 10.3934/math.2023754

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Research article

Numerical solution for the system of Lane-Emden type equations using cubic B-spline method arising in engineering

1.
Department of Mathematics, Jadara University, Irbid 21110, Jordan
2.
Department of Mathematics, Zarqa University, Zarqa 13110, Jordan

Received: 12 February 2023 Revised: 09 April 2023 Accepted: 11 April 2023 Published: 20 April 2023
MSC : 34K32, 34K34

In this study, we develop a collocation method based on cubic B-spline functions for effectively solving the system of Lane-Emden type equations arising in physics, star structure, and astrophysics. To overcome the singularity behavior of the considered system at τ = 0, we apply the L'Hôpital rule. Furthermore, we have carried out a convergence analysis of the proposed method and have demonstrated that it has a second-order convergence. To demonstrate the effectiveness, accuracy, simplicity, and practicality of the method, five test problems are solved numerically and the maximum absolute errors of the proposed method are compared with those of some existing methods.
- cubic spline,
- cubic B-spline,
- Lane-Emden equation,
- differential equations,
- initial value problem
Citation: Osama Ala'yed, Rania Saadeh, Ahmad Qazza. Numerical solution for the system of Lane-Emden type equations using cubic B-spline method arising in engineering[J]. AIMS Mathematics, 2023, 8(6): 14747-14766. doi: 10.3934/math.2023754

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Abstract

In this study, we develop a collocation method based on cubic B-spline functions for effectively solving the system of Lane-Emden type equations arising in physics, star structure, and astrophysics. To overcome the singularity behavior of the considered system at τ = 0, we apply the L'Hôpital rule. Furthermore, we have carried out a convergence analysis of the proposed method and have demonstrated that it has a second-order convergence. To demonstrate the effectiveness, accuracy, simplicity, and practicality of the method, five test problems are solved numerically and the maximum absolute errors of the proposed method are compared with those of some existing methods.

References

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