Lucas polynomial solution of nonlinear differential equations with variable delays

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Gümgüm S., Savaşaneril N. B., Kürkҫü Ö. K., Sezer M.

Hacettepe Journal of Mathematics and Statistics, cilt.49, sa.2, ss.553-564, 2020 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 2
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.460975
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.553-564
  • Anahtar Kelimeler: Lucas polynomials and series, Matrix and collocation methods, Nonlinear delay differential equations, Variable delays
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

In this study, a novel matrix method based on Lucas series and collocation points has been used to solve nonlinear differential equations with variable delays. The application of the method converts the nonlinear equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Lucas coefficients. The method is tested on three problems to show that it allows both analytical and approximate solutions.