The Homotopy Analytic Solutions for a Class of Jamming Transition Problem in Traffic Flow

Xiang Lin Han; Cheng Ouyang

doi:10.4028/www.scientific.net/AMM.444-445.1787

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 444-445The Homotopy Analytic Solutions for a Class of...

The Homotopy Analytic Solutions for a Class of Jamming Transition Problem in Traffic Flow

Abstract:

By choosing deferent initial approximation solutions and deferent linear operators, the nonlinear equation of the jamming transition problem (JTP), which is based on the Lorentz system, in traffic flow is discussed. The approximation solutions of the JTP are obtained using the homotopy analysis method (HAM). The method of choosing the linear operators and the initial approximation solutions, the corresponding residual errors and the influence of the boundary condition to the solution are studied respectively. By comparing the present results with the previous related studies, the conclusion is drawn that the HAM is superior to the differential transform method. The correctness of the theoretical analysis is confirmed by numerical simulation and the analysis of the residual errors.

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Periodical:

Applied Mechanics and Materials (Volumes 444-445)

Pages:

1787-1792

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.444-445.1787

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Online since:

October 2013

Authors:

Xiang Lin Han, Cheng Ouyang

Keywords:

Approximate Solution, Boundary Condition, Homotopy Analysis Method, Nonlinear Problem, Residual Error

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