Fredholm İntegro Diferansiyel Denklemin Sayısal Çözümü için Alternatif Bir Yöntem

Öz

Bu çalışmada, birinci mertebeden lineer Fredholm integro diferansiyel denklem için başlangıç değer problemini ele alıyoruz. Bu problemin nümerik çözümü için düzgün şebekede bir yeni fark şeması inşa ediyoruz. Bu şema, kalan terimi integral biçiminde olan interpolasyon quadratür formülleri ve üstel baz fonksiyonunu içeren integral özdeşliklerinden meydana gelmektedir. Metodun ayrık maksimum normda birinci mertebeden yakınsaklığı ispatladık. Ayrıca, hem sunulan metot hem de Euler metodu kullanılarak bir örnek çözüldü ve hesaplanan sonuçlar kaşılaştırıldı.

Anahtar Kelimeler

• Fredholm integro-diferansiyel denklem,başlangıç-değer problemi,sonlu fark metodu,hata değerlendirmesi

An Alternative Method for Numerical Solution of Fredholm Integro Differential Equation

Öz

In this paper, we consider a linear first order Fredholm integro differential equation with initial condition. To solve this problem numerically, we construct a
new difference scheme on a uniform mesh. The scheme is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. We prove that the method is
first order convergence in the discrete maximum norm. Moreover, a numerical example is solved using both the presented method and the Euler method and compared the computed results.

Anahtar Kelimeler

• Fredholm integro-differential equation,initial value problem,finite difference method,error estimate

Kaynakça

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