A Computational Method for Volterra Integro-Differential Equation

Bu çalışmada, lineer birinci mertebeden Volterra integro-diferansiyel denklem içeren başlangıç değer problemini ele almaktayız. Bu problemi nümerik olarak çözmek için yeni bir sonlu fark metodu veriyoruz. Bu metot, kalan terimi integral biçiminde olan interpolasyon quadratür formülleri ve üstel baz fonksiyonunu içeren integral özdeşliklerinden meydana gelmektedir. Ayrıca, bu metodun hata analizinin bir sonucu olarak, ayrık maksimum normda birinci mertebeden yakınsaklığı ispatlandı. Son olarak, elde edilen teorik sonuçları destekleyen nümerik örnek verildi.

Anahtar Kelimeler:

Başlangıç-Değer Problemi, Hata Değerlendirmesi, Sonlu Fark Metodu, Volterra İntegro-Diferansiyel Denklem

A Computational Method for Volterra Integro-Differential Equation

In this paper, we examine the initial value problem for a linear first order Volterra integro-differential equation. In order to solve the problem computationally, we present a novel finite difference method, which is based on the method of integral identities with the use of the basis functions and interpolating quadrature rules with remainder term in integral form. Furthermore, as a consequence of error analysis the method is proved to be first-order convergent in the discrete maximum norm. Finally, an example is provided to support our theoretical results.

Keywords:

Error Estimate, Finite Difference Method, Initial Value Problem, Volterra Integro-Differential Equation,

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