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Dergiler / 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
Sayfa
—
Yayın Tarihi
2022-06-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:By using implicit difference rules and composite numerical quadrature rules, the difference scheme is established on a Shishkin mesh.
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Sonuç & Katkı:The stability and convergence of the proposed scheme are analyzed and two examples are solved to display the advantages of the presented technique.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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