A Computational Method for Volterra Integro-Differential Equation

Year 2018, Volume: 11 Issue: 3, 347 - 352, 30.12.2018

Erkan Çimen

https://doi.org/10.18185/erzifbed.435331

Cited By: 3

Abstract

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.

Keywords

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

A Computational Method for Volterra Integro-Differential Equation

Abstract

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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