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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 3

A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh

Musa Çakır(VAN YÜZÜNCÜ YIL ÜNİVERSİTESİ)0000-0002-1979-570X
Baransel Güneş(VAN YÜZÜNCÜ YIL ÜNİVERSİTESİ)0000-0002-3265-8881
Pages
—
Publication Date
2022-06-01
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AI Summary & Key Takeaways

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

The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this research, the finite difference method is used to solve the initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity.
📊
Key Findings & Data:By using implicit difference rules and composite numerical quadrature rules, the difference scheme is established on a Shishkin mesh.
💡
Conclusion & Impact:The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:difference scheme · error estimate · Fredholm integro-differential equation

Abstract

In this research, the finite difference method is used to solve the initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit difference rules and composite numerical quadrature rules, the difference scheme is established on a Shishkin mesh. The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.

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Cite This Article

Çakır, M., Güneş, B. (2022). A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 3. https://doi.org/10.15672/hujms.950075

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