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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 2

Lucas polynomial solution of nonlinear differential equations with variable delays

Ömür Kıvanç Kürkçü
Mehmet Sezer
Sevin Gümgüm
Nurcan Baykuş Savaşaneril
Pages
553–564
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The method is tested on three problems to show that it allows both analytical and approximate solutions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:The method is tested on three problems to show that it allows both analytical and approximate solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Nonlinear delay differential equations · Variable delays · Matrix and collocation methods

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.

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Cite This Article

Kürkçü, Ö. K., Sezer, M., Gümgüm, S., Savaşaneril, N. B. (2022). Lucas polynomial solution of nonlinear differential equations with variable delays. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 2, 553–564. https://ajindex.com/articles/529667

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