Survey of the Layer Behaviour of the Singularly Perturbed Fredholm Integro-Differential Equation

Abstract

The work handles a second order linear singularly perturbed Fredholm integro differential equation. The qualitative analysis of such problems is quite difficult due to the rapid change in behavior of the solution within the boundary layer. In this study, asymptotic estimates for the solution and its first and second derivatives of the Fredholm integro differential equation with a boundary layer have been presented. The obtained estimates have significance in their contribution to the development and evaluation of appropriate approximate methods in mathematical modeling and analysis. Furthermore, the presented example provides support for the validity of the theoretical results and the accuracy of the estimates.

Keywords

• Asymptotic estimate
• Boundary layer
• Singular perturbation

Singüler Pertürbe Özellikli Fredholm İntegro Diferansiyel Denkleminin Katman Davranışının İncelenmesi

Abstract

Çalışma, ikinci mertebeden lineer singüler pertürbe özellikli Fredholm integro diferansiyel denklemini ele almaktadır. Bu tür problemlerin niteliksel analizi, çözümün sınır katmanlarındaki davranışının hızlı değişmesi nedeniyle oldukça zordur. Bu çalışmada sınır katmanlı Fredholm integro diferansiyel denkleminin çözümü ve çözümün birinci ve ikinci türevleri için asimptotik değerlendirmeler sunulmuştur. Elde edilen değerlendirmeler, matematiksel modelleme ve analizde uygun yaklaşık yöntemlerin geliştirilmesine ve değerlendirilmesine katkı sağlaması açısından önem taşımaktadır. Ayrıca sunulan örnek, teorik sonuçların geçerliliğine ve değerlendirmelerin doğruluğuna destek sağlamaktadır.

Keywords

• Asimptotik değerlendirme
• Sınır katmanı
• Singüler pertürbasyon

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