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交通拥堵相变问题的同伦分析法

韩祥临 欧阳成 宋涛 戴孙圣

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交通拥堵相变问题的同伦分析法

韩祥临, 欧阳成, 宋涛, 戴孙圣

The homotopy analysis method for a class of jamming transition problem in traffic flow

Han Xiang-Lin, Ouyang Cheng, Song Tao, Dai Sun-Sheng
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  • 利用同伦分析法研究了一类基于洛伦兹系统的交通拥堵相变问题的非线性方程. 通过选取不同的初始解和不同的线性算子,分别得到了问题的近似解和相应的残留误差. 通过与前人结果的比较得出,在研究该类问题时同伦分析法优于微分变换法; 在应用同伦分析法时,要选取尽可能接近原算子线性部分作为线性算子. 本文还给出了一种新的初始解选取方法(双同伦分析法). 数值模拟的结果证实了理论分析的正确性.
    Using the homotopy analysis method (HAM), the nonlinear equation of the jamming transition problem (JTP) in traffic flow is discussed, which is based on the Lorentz system. Through choosing different initial approximation solutions and different linear operators, approximation solutions of the JTP and the corresponding residual errors are obtained respectively. By comparing the present results with the previous related studies, the following conclusions can be drawn that the HAM is superior to the differential transform method; however, a linear operator should be chosen as best you can to approach the linear part of the original operator in using the HAM. A new method to choose the initial approximation solution (named double HAM) is given. The correctness of the theoretical analysis is verified by numerical simulation.
    • 基金项目: 国家自然科学基金(批准号: 11071205)和浙江省自然科学基金(批准号: LY13A010005, Y6110502)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11071205), and the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LY13A010005, Y6110502).
    [1]

    Orosz G, Wilson R E, Stépán G 2010 Phil. Trans. Math. Phys. Eng. Sci. 368 4455

    [2]

    Helbing D, Tilch B 1998 Phys. Rev. E 58 133

    [3]

    Wagner P 2011 Eur. Phys. J. B 84 713

    [4]

    Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 物理学报 55 634]

    [5]

    Ge H X, Han X L 2006 Physica A 371 667

    [6]

    Han X L, Jiang C Y, Ge H X, Dai S Q 2007 Acta Phys. Sin. 56 4383 (in Chinese) [韩祥临, 姜长元, 葛红霞, 戴世强 2007 物理学报 56 4383]

    [7]

    Jiang R, Wu Q S 20015 Eur. Phys. J. B 46 581

    [8]

    Tang C F, Jiang R, Wu Q S 2007 Phys. A 377 641

    [9]

    Olemskoi A I, Khomenko A V 1996 Am. Inst. Phys. 83 1180

    [10]

    Ganji S S, Barari A, Ibsen L B, Domairry D 2012 Cent. Eur. J. Oper. Res. 20 87

    [11]

    Ganji S S, Barari A, Najafi M, Domairry D 2011 Can. J. Phys. 89 729

    [12]

    Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199

    [13]

    Helbing D R 2001 Mod. Phys. 73 1067

    [14]

    Li X L, Song T, Kuang H, Dai S Q 2008 Chin. Phys. B 17 3014

    [15]

    Nagatani T 1998 Phys. Rev. E 58 4271

    [16]

    Olemskoi A I, Khomenko A V 1996 J. Exp. Theor. Phys. 83 1180

    [17]

    Olemskoi A I, Khomenko A V 2001 Phys. Rev. E 63 036116

  • [1]

    Orosz G, Wilson R E, Stépán G 2010 Phil. Trans. Math. Phys. Eng. Sci. 368 4455

    [2]

    Helbing D, Tilch B 1998 Phys. Rev. E 58 133

    [3]

    Wagner P 2011 Eur. Phys. J. B 84 713

    [4]

    Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 物理学报 55 634]

    [5]

    Ge H X, Han X L 2006 Physica A 371 667

    [6]

    Han X L, Jiang C Y, Ge H X, Dai S Q 2007 Acta Phys. Sin. 56 4383 (in Chinese) [韩祥临, 姜长元, 葛红霞, 戴世强 2007 物理学报 56 4383]

    [7]

    Jiang R, Wu Q S 20015 Eur. Phys. J. B 46 581

    [8]

    Tang C F, Jiang R, Wu Q S 2007 Phys. A 377 641

    [9]

    Olemskoi A I, Khomenko A V 1996 Am. Inst. Phys. 83 1180

    [10]

    Ganji S S, Barari A, Ibsen L B, Domairry D 2012 Cent. Eur. J. Oper. Res. 20 87

    [11]

    Ganji S S, Barari A, Najafi M, Domairry D 2011 Can. J. Phys. 89 729

    [12]

    Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199

    [13]

    Helbing D R 2001 Mod. Phys. 73 1067

    [14]

    Li X L, Song T, Kuang H, Dai S Q 2008 Chin. Phys. B 17 3014

    [15]

    Nagatani T 1998 Phys. Rev. E 58 4271

    [16]

    Olemskoi A I, Khomenko A V 1996 J. Exp. Theor. Phys. 83 1180

    [17]

    Olemskoi A I, Khomenko A V 2001 Phys. Rev. E 63 036116

计量
  • 文章访问数:  5269
  • PDF下载量:  463
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-04-08
  • 修回日期:  2013-05-20
  • 刊出日期:  2013-09-05

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