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Title: A neural computational method for solving renewal delay integro-differential equations constrained by the half-line
Authors: Kürkçü, Ömür Kıvanç
Keywords: Delay forces
Error bound
Infinite boundary
Neural computation
Renewal equation
Issue Date: 2022
Publisher: Springer Heidelberg
Abstract: This study aims to solve the renewal delay integro-differential equations constrained by the half-line, introducing a computational method composed of the matrix relations of the Stieltjes-Wigert polynomials at the collocation points. In order to mathematically interpret their robust integral part, the method is also fed neurally by the Stieltjes-Wigert polynomials and a hybrid polynomial dependent upon the alteration of the Taylor and exponential polynomial bases. Thus, the method easily gathers the matrix relations into a matrix equation and immediately produces a desired solution. An error bound analysis is established to discuss the accuracy of the method by employing the collaboration of the mentioned polynomials. A population model with time-lags (delays), the detection of the displaced atoms versus kinetic energy, an integral delay equation, and a delayed problem with functional kernel are firstly treated by the method. Consequently, it is evident that the method presents a novel consistent approach and is directly programmable on a mathematical software thanks to its neural structure.
Description: Article; Early Access
ISSN: 2008-1359
Appears in Collections:Mühendislik ve Doğa Bilimleri Fakültesi Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collections
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collections

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