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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2018 / Cilt: 11 - Sayı: 3

A Computational Method for Volterra Integro-Differential Equation

Erkan ÇİMEN
Pages
347–352
Publication Date
2018-12-30
DOI
—
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AI Summary & Key Takeaways

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

Finally, an example is provided to support our theoretical results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we examine the initial value problem for a linear first order Volterra integro-differential equation.
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Key Findings & Data:In order to solve the problem computationally, we present a novel finite difference method, which is based on the method of integral identities with the use of the basis functions and interpolating quadrature rules with remainder term in integral form.
💡
Conclusion & Impact:Finally, an example is provided to support our theoretical results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Başlangıç-Değer Problemi · Hata Değerlendirmesi · Sonlu Fark Metodu

Abstract

In this paper, we examine the initial value problem for a linear first order Volterra integro-differential equation. In order to solve the problem computationally, we present a novel finite difference method, which is based on the method of integral identities with the use of the basis functions and interpolating quadrature rules with remainder term in integral form. Furthermore, as a consequence of error analysis the method is proved to be first-order convergent in the discrete maximum norm. Finally, an example is provided to support our theoretical results.

Özet

Bu çalışmada, lineer birinci mertebeden Volterra integro-diferansiyel denklem içeren başlangıç değer problemini ele almaktayız. Bu problemi nümerik olarak çözmek için yeni bir sonlu fark metodu veriyoruz. Bu metot, kalan terimi integral biçiminde olan interpolasyon quadratür formülleri ve üstel baz fonksiyonunu içeren integral özdeşliklerinden meydana gelmektedir. Ayrıca, bu metodun hata analizinin bir sonucu olarak, ayrık maksimum normda birinci mertebeden yakınsaklığı ispatlandı. Son olarak, elde edilen teorik sonuçları destekleyen nümerik örnek verildi.

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Cite This Article

ÇİMEN, E. (2018). A Computational Method for Volterra Integro-Differential Equation. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 11 - Sayı: 3, 347–352. https://ajindex.com/articles/234429

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References (12)

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