WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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Article Citation - WoS: 5Citation - Scopus: 6Solution of Jamming Transition Problem Using Adomian Decomposition Method(Emerald Group Publishing Ltd, 2018-08-08) Senturk, Erman; Coskun, Safa Bozkurt; Atay, Mehmet TarikPurpose The purpose of the study is to obtain an analytical approximate solution for jamming transition problem (JTP) using Adomian decomposition method (ADM). Design/methodology/approach In this study, the jamming transition is presented as a result of spontaneous deviations of headway and velocity that is caused by the acceleration/breaking rate to be higher than the critical value. Dissipative dynamics of traffic flow can be represented within the framework of the Lorenz scheme based on the car-following model in the one-lane highway. Through this paper, an analytical approximation for the solution is calculated via ADM that leads to a solution for headway deviation as a function of time. Findings A highly nonlinear differential equation having no exact solution due to JTP is considered and headway deviation is obtained implementing a number of different initial conditions. The results are discussed and compared with the available data in the literature and numerical solutions obtained from a built-in numerical function of the mathematical software used in the study. The advantage of using ADM for the problem is presented in the study and discussed on the basis of the results produced by the applied method. Originality/value This is the first study to apply ADM to JTP.Article Axial Free Vibration Analysis of a Tapered Nanorod Using Adomian Decomposition Method(Techno-Press, 2025) Coskun, Safa B.; Kara, Ozge; Atay, Mehmet T.; Coçkun, Safa B.This study aimed to conduct an analysis of the axial free vibration of tapered nanorods based on nonlocal elasticity theory. The small-scale effect on the free axial vibration of a tapered nanorod was studied employing the Adomian decomposition method (ADM) and the finite difference method (FDM) as a checking tool where a contradiction existed between the results of this study and available results in one highly cited work in the literature, which was used for comparison purposes in this work. Different boundary conditions for the nanorod were considered: fixed-fixed nanorod, fixed-free nanorod, and fixed-linear spring nanorod. The governing equation of the problem is a variable coefficient differential equation for which analytical solutions are strictly limited. For this type of problem, analytical approximate methods are effective, and there are many studies available in the literature on the application of these methods to solve linear/nonlinear ordinary/partial differential equations. ADM is one of the methods and was successfully used in this study to analyze the free vibration of nanorods. The results obtained in this study have shown that the presented technique is so powerful and has potential for applications in nanomechanics based on nonlocal elasticity theory.