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Interpolated variational iteration method for solving the jamming transition problem

机译：插值变分迭代法求解干扰过渡问题

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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.
机译：这项研究的目的是使用插值变分迭代方法（IVIM）提出一种基于解析的数值方法来解决干扰转移问题（JTP）。该方法消除了解析变分迭代技术中表达式的解析积分的困难，并提供了具有解析精度的数值结果。可以通过Lorenz系统将JTP转换为非线性非保守振荡器，在该系统中，由加速/断裂速率引起的车速和速度的自发偏差表示干扰跃迁高于临界值。由于方程中存在非线性，因此JTP的最终控制方程没有精确的解决方案。该问题以前曾尝试通过包括分析变分迭代技术在内的分析逼近方法半解析地解决。这项研究的结果表明，IVIM解与数学软件提供的数值解非常吻合。介绍了根据控制方程有两种不同公式的IVIM。根据使用IVIM执行的分析，确定所需的解决方案顺序和达成良好协议的时间步骤数。 （C）2019国际模拟数学与计算机协会（IMACS）。由Elsevier B.V.发布。保留所有权利。

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