Adaptive hybrid numerical schemes with singularity treatment for third-order Lane-Emden type equations

Articles in Press

Document Type : Research Article

Author

Mehdi Fazli

Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.

10.22067/ijnao.2026.97038.1812

Abstract

This paper introduces two hybrid algorithms with variable step sizes (PVSHM) designed for the efficient numerical solution of third-order initial value problems (IVPs) governed by Lane Emden-type equations (LETEs). These equations frequently arise in various scientific and engineering fields, including astrophysics, fluid dynamics, and chemical engineering, where they serve as fundamental mathematical models for complex physical systems. The proposed methods utilize three internal interpolation points and incorporate carefully constructed formulations to remove the singularity that appears at the origin. To ensure both high accuracy and computational efficiency, the PVSHM operates within a variable step-size framework supported by an adaptive local error control strategy, which maintains truncation errors within predefined tolerances. Extensive numerical experiments validate the accuracy, stability, and computational effectiveness of the proposed algorithms, confirming their ability to efficiently solve a wide range of third-order LETE-based IVPs encountered in applied science and engineering contexts.

Keywords

Lane-Emden type equations

Third-order initial value problems

Hybrid methods

Variable step-size algorithm

Adaptive error control

Subjects

• Numerical linear algebra and its applications

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