Approximate Solutions of the Lane-Emden Equations by LS-SVM Method

Süleyman Şengül; Hasan Halit Tali

doi:10.47000/tjmcs.1609938

Approximate Solutions of the Lane-Emden Equations by LS-SVM Method

Abstract

In this study, approximate solutions of the Lane-Emden differential equation, which plays an important role in the literature, were obtained using the Least Squares Support Vector Machines (LS-SVM) method for both linear and nonlinear cases. The Collocation method was employed to define the constraints in the solution process. The system of equations obtained in the linear case was solved directly to determine the unknown parameters, while the Newton-Raphson method was used to solve the nonlinear equation system. The approximate solutions obtained in the applications considered in this study were compared with the exact solution for the linear case; with the analytical solution for the nonlinear case; and with the Adomian Decomposition Method (ADM) in the final application where no analytical solution exists. The results show that the numerical solutions obtained using the LS-SVM method are highly accurate and consistent with the reference results.

Keywords

References

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Details

Primary Language

English

Subjects

Machine Learning (Other), Numerical Solution of Differential and Integral Equations

Journal Section

Research Article

Authors

Süleyman Şengül
0000-0002-0359-4137
Türkiye

Hasan Halit Tali ^*
0000-0002-1704-3694
Türkiye

Publication Date

February 23, 2026

Submission Date

December 30, 2024

Acceptance Date

October 22, 2025

Published in Issue

Year 2026 Volume: 18 Number: 1

DOI

https://doi.org/10.47000/tjmcs.1609938

IZ

https://izlik.org/JA65CC27SY

Cite

RIS / Bibtex

APA

Şengül, S., & Tali, H. H. (2026). Approximate Solutions of the Lane-Emden Equations by LS-SVM Method. Turkish Journal of Mathematics and Computer Science, 18(1), 11-23. https://doi.org/10.47000/tjmcs.1609938

AMA

1.Şengül S, Tali HH. Approximate Solutions of the Lane-Emden Equations by LS-SVM Method. TJMCS. 2026;18(1):11-23. doi:10.47000/tjmcs.1609938

Chicago

Şengül, Süleyman, and Hasan Halit Tali. 2026. “Approximate Solutions of the Lane-Emden Equations by LS-SVM Method”. Turkish Journal of Mathematics and Computer Science 18 (1): 11-23. https://doi.org/10.47000/tjmcs.1609938.

EndNote

Şengül S, Tali HH (February 1, 2026) Approximate Solutions of the Lane-Emden Equations by LS-SVM Method. Turkish Journal of Mathematics and Computer Science 18 1 11–23.

IEEE

[1]S. Şengül and H. H. Tali, “Approximate Solutions of the Lane-Emden Equations by LS-SVM Method”, TJMCS, vol. 18, no. 1, pp. 11–23, Feb. 2026, doi: 10.47000/tjmcs.1609938.

ISNAD

Şengül, Süleyman - Tali, Hasan Halit. “Approximate Solutions of the Lane-Emden Equations by LS-SVM Method”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 11-23. https://doi.org/10.47000/tjmcs.1609938.

JAMA

1.Şengül S, Tali HH. Approximate Solutions of the Lane-Emden Equations by LS-SVM Method. TJMCS. 2026;18:11–23.

MLA

Şengül, Süleyman, and Hasan Halit Tali. “Approximate Solutions of the Lane-Emden Equations by LS-SVM Method”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 11-23, doi:10.47000/tjmcs.1609938.

Vancouver

1.Süleyman Şengül, Hasan Halit Tali. Approximate Solutions of the Lane-Emden Equations by LS-SVM Method. TJMCS. 2026 Feb. 1;18(1):11-23. doi:10.47000/tjmcs.1609938