Interpolated Variational Iteration Method for Solving the Jamming Transition Problem

Abstract

The purpose of this study is to present an analytical based numerical solution for Jamming Transition Problem (JTP) using Interpolated Variational Iteration Method (IVIM). The method eliminates the difficulties on analytical integration of expressions in analytical variational iteration technique and provides numerical results with analytical accuracy. JTP may be transformed into a nonlinear non-conservative oscillator by Lorenz system in which jamming transition is presented as spontaneous deviations of headway and velocity caused by the acceleration/breaking rate to be higher than the critical value. The resulting governing equation of JTP has no exact solution due to existing nonlinearities in the equation. The problem was previously attempted to be solved semi-analytically via analytical approximation methods including analytical variational iteration technique. The results of this study show that IVIM solutions agree very well with the numerical solution provided by the mathematical software. IVIM with two different formulation according to governing equation is introduced. Required order of the solution and number of time steps for a good agreement is determined according to the analyses performed using IVIM. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.