交通拥堵相变问题的同伦分析法

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. 关键词： 同伦分析法 交通拥堵 近似解 残留误差

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

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.
Keywords： homotopy analysis method traffic jam approximate solution residual error