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, vol.49, no.2, pp.553-564, 2020 (SCI-Expanded, Scopus, TRDizin) identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.15672/hujms.460975
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.553-564
  • Keywords: Lucas polynomials and series, Matrix and collocation methods, Nonlinear delay differential equations, Variable delays
  • Open Archive Collection: AVESIS Open Access Collection
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

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.