Nümerik İntegrasyon Metodu ile Singüler Pertürbe Problemlerin Yaklaşık Çözümü

Year 2022, Volume: 27 Issue: 3, 612 - 618, 25.12.2022

Derya Arslan

https://doi.org/10.53433/yyufbed.1094184

Abstract

Bu çalışmada, singüler pertürbe Volterra integro-diferansiyel denklemlerin yaklaşık çözümü için nümerik integrasyon yöntemi uygulanır. İlk olarak düzgün bir şebeke üzerinde sonlu fark metodu ile başlanır daha sonra integraller için trapez metodu kullanılır. Buradan elde edilen denklem sistemi Thomas algoritması ile çözülür. Önerilen yöntemin doğruluğunu ve ekonomikliğini ortaya koyan bir örnek sunulur.

Keywords

Nümerik integrasyon metodu, Singüler pertürbe problem, Sonlu fark metodu, Trapez metodu, Volterra integro-diferansiyel denklem

Approximate Solution of Singularly Perturbed Problems with Numerical Integration Method

Abstract

In this study, the numerical integration method is performed for approximate solution of the singularly perturbed Volterra integro-differential equations. Firstly, it starts with the finite difference method on the uniform mesh points, then the trapezoidal method is used for integrals. The system of equations obtained here is solved with the Thomas algorithm. An example is presented that demonstrates the accuracy and economy of the proposed method.

Keywords

Finite difference method, Numerical integration method, Singularly perturbed problem, Trapezoidal method, Volterra integro-differential equation

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