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Journals / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 - Sayı: 2

An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation

Muhammet Enes DURMAZ
Ömer YAPMAN
Mustafa KUDU
Gabil AMİRALİ
Pages
326–339
Publication Date
2023-03-31
DOI
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AI Summary & Key Takeaways

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

Numerical results illustrating the preciseness and computationally attractiveness of the proposed method are presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The scope of this study is to establish an effective approximation method for linear first order singularly perturbed Volterra-Fredholm integro-differential equations.
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Key Findings & Data:The finite difference scheme is constructed on Shishkin mesh by using appropriate interpolating quadrature rules and exponential basis function.
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Conclusion & Impact:Numerical results illustrating the preciseness and computationally attractiveness of the proposed method are presented.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:finite difference methods · integro-differential equation · Shishkin mesh

Abstract

The scope of this study is to establish an effective approximation method for linear first order singularly perturbed Volterra-Fredholm integro-differential equations. The finite difference scheme is constructed on Shishkin mesh by using appropriate interpolating quadrature rules and exponential basis function. The recommended method is second order convergent in the discrete maximum norm. Numerical results illustrating the preciseness and computationally attractiveness of the proposed method are presented.

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Cite This Article

DURMAZ, M. E., YAPMAN, Ö., KUDU, M., AMİRALİ, G. (2023). An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 - Sayı: 2, 326–339. https://ajindex.com/articles/886283

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