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Journals / Karaelmas Fen ve Mühendislik Dergisi / 2026 / Cilt: 16 Sayı: 2

An Efficient Approach for Numerical Solution of Delay Differential Equation

Gecikmeli Diferansiyel Denklemin Nümerik Çözümü İçin Etkili Bir Yaklaşım

Erkan Çimen(VAN YÜZÜNCÜ YIL ÜNİVERSİTESİ)0000-0002-7258-192X
Neslişah Tekin(VAN YÜZÜNCÜ YIL ÜNİVERSİTESİ)0009-0008-5834-7425
Pages
106–116
Publication Date
2026-07-24
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AI Summary & Key Takeaways

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

Finally, a test problem is considered to demonstrate the accuracy and performance of the method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a new numerical scheme for solving the initial value problem for first order linear delay differential equations is proposed.
📊
Key Findings & Data:This scheme is constructed using the finite difference method on a uniform mesh using quadrature rules, with the remaining terms in integral form.
💡
Conclusion & Impact:Finally, a test problem is considered to demonstrate the accuracy and performance of the method.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Gecikmeli diferansiyel denklem · sonlu fark metodu · hata analizi

Abstract

In this paper, a new numerical scheme for solving the initial value problem for first order linear delay differential equations is proposed. This scheme is constructed using the finite difference method on a uniform mesh using quadrature rules, with the remaining terms in integral form. The scheme is proven to achieve second-order convergence in the discrete maximum norm. Finally, a test problem is considered to demonstrate the accuracy and performance of the method.

Özet

Bu çalışmada, birinci mertebeden lineer gecikmeli diferansiyel denklemler için başlangıç değer probleminin çözümü için yeni bir nümerik şema önerilmiştir. Bu şema, kalan terimleri integral formda olan quadratür kuralları kullanarak düzgün bir şebeke üzerinde sonlu farklar yöntemi ile oluşturulmuştur. Şemanın ayrık maksimum normda ikinci mertebeden yakınsamaya ulaştığı kanıtlanmıştır. Son olarak, yöntemin doğruluğunu ve performansını göstermek için bir test problemi ele alınmıştır.

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Cite This Article

Çimen, E., Tekin, N. (2026). An Efficient Approach for Numerical Solution of Delay Differential Equation. Karaelmas Fen ve Mühendislik Dergisi, Cilt: 16 Sayı: 2, 106–116. https://doi.org/10.7212/karaelmasfen.1870923

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