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Differential transform method for mathematical modeling of jamming transition problem in traffic congestion flow

Author

Listed:
  • S. Ganji
  • A. Barari
  • L. Ibsen
  • G. Domairry

Abstract

In this paper we aim to find an analytical solution for jamming transition in traffic flow. Generally the Jamming Transition Problem (JTP) can be modeled via Lorentz system. So, in this way, the governing differential equation achieved is modeled in the form of a nonlinear damped oscillator. In current research the authors utilized the Differential Transformation Method (DTM) for solving the nonlinear problem and compared the analytical results with those ones obtained by the 4th order Runge-Kutta Method (RK4) as a numerical method. Further illustration embedded in this paper shows the ability of DTM in solving nonlinear problems when a so accurate solution is required. Copyright Springer-Verlag 2012

Suggested Citation

  • S. Ganji & A. Barari & L. Ibsen & G. Domairry, 2012. "Differential transform method for mathematical modeling of jamming transition problem in traffic congestion flow," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(1), pages 87-100, March.
    • Handle: RePEc:spr:cejnor:v:20:y:2012:i:1:p:87-100
    DOI: 10.1007/s10100-010-0154-7
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    References listed on IDEAS

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    1. He, Ji-Huan & Abdou, M.A., 2007. "New periodic solutions for nonlinear evolution equations using Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1421-1429.
    2. Kai Nagel, 1994. "Life Times Of Simulated Traffic Jams," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 567-580.
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    Cited by:

    1. Coşkun, Safa Bozkurt & Atay, Mehmet Tarık & Şentürk, Erman, 2019. "Interpolated variational iteration method for solving the jamming transition problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 481-493.

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