A Robust Semi-analytical Technique for Solving Third-order Non-linear Emden-Fowler Equations

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematical Sciences, P D Patel Institute of Applied Sciences, Charotar University of Science & Technology, Changa, Gujarat-388421, India.

2 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

Abstract

This study presents a robust semi-analytical algorithm for solving third-order nonlinear Emden--Fowler type equations, which frequently arise in astrophysics, chemical reactor theory, and mathematical physics. The proposed algorithm leverages the Differential Transform Method (DTM) to simplify the complexities introduced by nonlinear terms, transforming them into manageable algebraic equations. The novelty of this approach lies in its ability to handle singular behavior at $x=0$ while maintaining high computational efficiency and accuracy. Rigorous error analysis confirms the algorithm's rapid convergence and superior accuracy compared to existing methods. Numerical experiments validate the theoretical predictions, highlighting the algorithm's effectiveness and reliability in solving complex nonlinear differential equations.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 29 May 2026

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History

  • Receive Date: 29 April 2025
  • Revise Date: 27 April 2026
  • Accept Date: 25 May 2026

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