An improved car-following model with consideration of the lateral effect and its feedback control research

A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. A control signal including the velocity differences between the following vehicle and the target vehicle is introduced according to the feedback control theory. The stability condition for the new model is derived. Numerical simulation is used to demonstrate the advantage of the new model including the control signal; the results are consistent with the analytical ones     

An element-free Galerkin (EFG) method for generalized Fisher equations (GFE)

A generalized Fisher equation(GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance.The exact mathematical result of the GFE has been widely used in population dynamics and genetics,where it originated.Many researchers have studied the numerical solutions of the GFE,up to now.In this paper,we introduce an element-free Galerkin(EFG) method based on the moving least-square approximation to approximate positive solutions of the GFE from population dynamics.Compared with other numerical methods,the EFG method for the GFE needs only scattered nodes instead of meshing the domain of the problem.The Galerkin weak form is used to obtain the discrete equations,and the essential boundary conditions are enforced by the penalty method.In comparison with the traditional method,numerical solutions show that the new method has higher accuracy and better convergence.Several numerical examples are presented to demonstrate the effectiveness of the method.     

An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations

The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme.     

An element-free Galerkin （EFG） equations method for generalized Fisher （GFE）

A generalized Fisher equation （GFE） relates the time derivative of the average of the intrinsic rate of growth to its variance. The exact mathematical result of the GFE has been widely used in population dynamics and genetics, where it originated. Many researchers have studied the numerical solutions of the GFE, up to now. In this paper, we introduce an element-free Galerkin （EFG） method based on the moving least-square approximation to approximate positive solutions of the GFE from population dynamics. Compared with other numerical methods, the EFG method for the GFE needs only scattered nodes instead of meshing the domain of the problem. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. In comparison with the traditional method, numerical solutions show that the new method has higher accuracy and better convergence. Several numerical examples are presented to demonstrate the effectiveness of the method.     

A new control method based on the lattice hydrodynamic model considering the double flux difference

A new feedback control method is derived based on the lattice hydrodynamic model in a single lane. A signal based on the double flux difference is designed in the lattice hydrodynamic model to suppress the traffic jam. The stability of the model is analyzed by using the new control method. The advantage of the new model with and without the effect of double flux difference is explored by the numerical simulation. The numerical simulations demonstrate that the traffic jam can be alleviated by the control signal.     

考虑前后车效应的反馈控制跟驰模型

本文中,在优化速度模型的基础上,提出一个计及跟随车与当前车车头间距的跟驰模型.从控制论角度出发,对模型进行稳定性分析,得到了模型的稳定性条件.同时,在新模型中引入了反馈控制信息,考虑当前车与前后方车辆之间的速度差.对模型进行线性分析后得到小扰动不会导致交通堵塞的条件.在开放边界条件下,对两个模型进行数值模拟,结果表明在控制信号下,车辆速度波动明显减小,拥堵现象得到有效缓解.从而证实反馈控制信号对缓解交通拥堵的重要作用.     

Considering Backward Effect in Coupled Map Car-Following Model

Based on the pioneer work of Konishi et al., a new control method is proposed to suppress the traffic congestion in the coupled map （CM） car-following model under open boundary condition. The influence of the following car to the system has been considered. Our method and that presented by Konishi et al. [Phys. Rev. E 60 （1999） 4000] are compared. Although both the methods could suppress the traffic jam, the simulation results show that the temporal behavior obtained by ours is better than that proposed by the Konishi＇s et al. The simulation results are consistent with the theoretical analysis.     

A control method applied to mixed traffic flow for the coupled-map car-following model

In light of previous work [Phys. Rev. E 60 4000 （1999）], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.     

A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.     

双参数非线性奇摄动边值问题的角层解

本研究含双参数的拟线性微分方程的非线性奇摄动边值问题，利用微分不等式原理，得到问题的一个渐近解并对余项作了估计。