AVersatile Spectral Matrix Collocation Method for Tackling Bratu, Riccati, and Higher Order Linear and Nonlinear Differential Equations Containing Delay Variables

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Baykuş Savaşaneril N., Çevik M.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.14, ss.1-14, 2025 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/mma.70110
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-14
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

 This study presents a numerical matrix collocation method for solving Bratu equations, Riccati equations, and high-order lin ear/nonlinear differential equations with delay variables—all of which hold significant importance in the literature. Addressing these widely studied problems from a novel perspective, we develop a new technique that transforms each problem into an algebraic matrix equation based on Lucas polynomials. The proposed method constructs approximate solutions using Lucas poly nomialswithconventionalorderingpoints, whichformthefoundationalbasisofourapproach.Foreachproblemtype,weexplore different solution scenarios and provide tailored computational strategies. Numerical results, presented in tables and figures, demonstrate consistency and effectiveness by comparing our method with existing approaches for various ranking points. MSC2020Classification: 33C45, 65D32, 65F10, 34A34, 35J60, 34K11, 34K35