A Chelyshkov-based spectral homotopy analysis method for singular nonlinear Lane-Emden-type equations
Networks and Heterogeneous Media, vol.21, no.3, pp.943-967, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 21 Issue: 3
- Publication Date: 2026
- Doi Number: 10.3934/nhm.2026039
- Journal Name: Networks and Heterogeneous Media
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, MathSciNet, zbMATH
- Page Numbers: pp.943-967
- Keywords: Chelyshkov polynomials, Lane-Emden equation, nonlinear equations, spectral homotopy analysis method, spectral methods
- Istanbul Gelisim University Affiliated: Yes
Abstract
An enhanced numerical technique for solving the Lane-Emden equation is developed using the spectral homotopy analysis method (SHAM) with Chelyshkov polynomials and Gauss-Lobatto collocation nodes. The numerical results, including absolute errors and comparisons with the exact solution, demonstrate the convergence behavior and accuracy of the proposed approach. The results show that the Chelyshkov-based SHAM provides an effective framework for the numerical treatment of Lane-Emden-type problems.