Solution of jamming transition problem using adomian decomposition method

Abstract

Purpose 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.

Analysis of the motion of a rigid rod on a circular surface using interpolated variational iteration method

“…In last decades, some analytical approximate methods and their modifications were suggested by researchers for solving nonlinear problems such as Adomian decomposition method [6,7,8], variational iteration method (VIM) [8,9,10,13], differential transform method [8,11], homotopy perturbation method [12, 13,14], harmonic balance method [15], incremental harmonic balance method [16], Newton-harmonic balance method [17], variational approach method [18], amplitude-frequency formulation [19][20][21], energy balance method [20], max-min approach [21]. Variety of methods to solve nonlinear problems provide more reliable results for the modal parameter on the vibration period.…”