Based on the optimal velocity(OV)model,a new car-following model for traffic flow with the consideration of the driver's forecast effect(DFE)was proposed by Tang et al.,which can be used to describe some complex t...Based on the optimal velocity(OV)model,a new car-following model for traffic flow with the consideration of the driver's forecast effect(DFE)was proposed by Tang et al.,which can be used to describe some complex traffic phenomena better.Using an asymptotic approximation between the headway and density,we obtain a new macro continuum version of the car-following model with the DFE.The linear stability theory is applied to derive the neutral stability condition.The Korteweg–de Vries equation near the neutral stability line is given by nonlinear analysis and the corresponding solution for the traffic density wave is derived.展开更多
The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin （EFG） method, which is based on the moving least-square approximation. Compared w...The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin （EFG） method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem. It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. In this method, the first-order time derivative is replaced by the Caputo fractional derivative of order α（0 〈 α≤ 1）. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions.展开更多
基金by the National Natural Science Foundation of China under Grant Nos 11072117,10802042 and 60904068the Natural Science Foundation of Zhejiang Province under Grant Nos Y6110007 and Y6110502+1 种基金the K.C.Wong Magna Fund in Ningbo Universitythe Research Grant Council,Government of the Hong Kong Administrative Region,China,under Grant No CityU118708.
文摘Based on the optimal velocity(OV)model,a new car-following model for traffic flow with the consideration of the driver's forecast effect(DFE)was proposed by Tang et al.,which can be used to describe some complex traffic phenomena better.Using an asymptotic approximation between the headway and density,we obtain a new macro continuum version of the car-following model with the DFE.The linear stability theory is applied to derive the neutral stability condition.The Korteweg–de Vries equation near the neutral stability line is given by nonlinear analysis and the corresponding solution for the traffic density wave is derived.
基金Project supported by the National Natural Science Foundation of China(Grant No.11072117)the Natural Science Foundationof Zhejiang Province,China(Grant Nos.Y6110007and Y6110502)the K.C.Wong Magna Fund in Ningbo University,China
文摘The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin （EFG） method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem. It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. In this method, the first-order time derivative is replaced by the Caputo fractional derivative of order α（0 〈 α≤ 1）. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions.
