AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS

Dharmendra Kumar; Amit K. Barnwal

AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS

Abstract

In this article, we analyze collocation points and shifted Chebyshev polynomials based strategy to approximate the solution of the Lane-Emden type functional differential equations subjected to three-point boundary conditions. Shifted Chebyshev polynomials are used to reduce the problem into a matrix form, and then, collocation points are used to transform the matrix form into a system of nonlinear algebraic equations. The simplicity of the mathematical formulation and ease of code computation, demonstrate the accessibility and flexibility of the proposed numerical technique. The outcomes clearly show that the proposed approach achieves rapid convergence, exhibits a high level of computational efficiency, and delivers precise approximations. Finally, numerous examples are included to illustrate and confirm the applicability, validity and superiority of the proposed approach over the existing methods.

Keywords

References

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Ordinary Differential Equations, Difference Equations and Dynamical Systems

Journal Section

Research Article

Authors

Dharmendra Kumar This is me
0009-0003-3909-4454
India

Amit K. Barnwal ^* This is me
0000-0003-3615-7723
India

Publication Date

June 9, 2026

Submission Date

April 24, 2025

Acceptance Date

February 5, 2026

Published in Issue

Year 2026 Volume: 16 Number: 6

IZ

https://izlik.org/JA24JZ77GP

Cite

RIS / Bibtex

APA

Kumar, D., & Barnwal, A. K. (2026). AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS. TWMS Journal of Applied and Engineering Mathematics, 16(6), 740-761. https://izlik.org/JA24JZ77GP

AMA

1.Kumar D, Barnwal AK. AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS. JAEM. 2026;16(6):740-761. https://izlik.org/JA24JZ77GP

Chicago

Kumar, Dharmendra, and Amit K. Barnwal. 2026. “AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS”. TWMS Journal of Applied and Engineering Mathematics 16 (6): 740-61. https://izlik.org/JA24JZ77GP.

EndNote

Kumar D, Barnwal AK (June 1, 2026) AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS. TWMS Journal of Applied and Engineering Mathematics 16 6 740–761.

IEEE

[1]D. Kumar and A. K. Barnwal, “AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS”, JAEM, vol. 16, no. 6, pp. 740–761, June 2026, [Online]. Available: https://izlik.org/JA24JZ77GP

ISNAD

Kumar, Dharmendra - Barnwal, Amit K. “AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS”. TWMS Journal of Applied and Engineering Mathematics 16/6 (June 1, 2026): 740-761. https://izlik.org/JA24JZ77GP.

JAMA

1.Kumar D, Barnwal AK. AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS. JAEM. 2026;16:740–761.

MLA

Kumar, Dharmendra, and Amit K. Barnwal. “AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 6, June 2026, pp. 740-61, https://izlik.org/JA24JZ77GP.

Vancouver

1.Dharmendra Kumar, Amit K. Barnwal. AN EFFICIENT NUMERICAL ALGORITHM FOR SOLVING THE LANE-EMDEN TYPE FUNCTIONAL BOUNDARY VALUE PROBLEMS. JAEM [Internet]. 2026 Jun. 1;16(6):740-61. Available from: https://izlik.org/JA24JZ77GP