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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

A fitted approximate method for a Volterra delay-integro-differential equation with initial layer

Gabil M. Amiraliyev
Ömer Yapman
Mustafa Kudu
Pages
1417–1429
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Numerical results are also given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study is concerned with the finite-difference solution of singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay.
📊
Key Findings & Data:The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form.
💡
Conclusion & Impact:Numerical results are also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Volterra delay-integro-differential equation · singular perturbation · finite difference

Abstract

This study is concerned with the finite-difference solution of singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. The method is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The emphasis is on the convergence of numerical method. It is shown that the method displays uniform convergence in respect to the perturbation parameter. Numerical results are also given.

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Cite This Article

Amiraliyev, G. M., Yapman, Ö., Kudu, M. (2022). A fitted approximate method for a Volterra delay-integro-differential equation with initial layer. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1417–1429. https://ajindex.com/articles/529749

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