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

Iranian Journal of Numerical Analysis and Optimization

مقاله 1، دوره 17، Issue 1 - شماره پیاپی 40، بهار 2027، صفحه 1-24   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2026.97038.1812

نویسنده

Mehdi Fazli^*

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

چکیده

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.

کلیدواژه‌ها

Lane-Emden type equations؛ Third-order initial value problems؛ Hybrid methods؛ Variable step-size algorithm؛ Adaptive error control