A Chelyshkov-based spectral homotopy analysis method for singular nonlinear Lane-Emden-type equations

Bouakkaz M., Arar N., Meflah M., Shah K., Abdalla B., Abdeljawad T.

Networks and Heterogeneous Media, cilt.21, sa.3, ss.943-967, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3934/nhm.2026039
  • Dergi Adı: Networks and Heterogeneous Media
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Compendex, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.943-967
  • Anahtar Kelimeler: Chelyshkov polynomials, Lane-Emden equation, nonlinear equations, spectral homotopy analysis method, spectral methods
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.