A wavelet-galerkin method for the kinematic wave model of traffic flow

Abstract

In this paper, a wavelet-Galerkin formulation with domain transformation is applied to solve the kinematic wave model of traffic flow. A domain transformation method is employed to resolve the constraints imposed on the solution variables. This avoids the problem of generating invalid solution of traffic states as with conventional numerical schemes for the wave model. With the localized scaling function or wavelet, the method is also capable of capturing the shock wave in the traffic model. Moreover, due to the localized characteristics of wavelets, the bandwidths of matrices are usually very small. Therefore, a robust band-matrix solver can be employed to enhance computational efficiency. Numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2000 John Wiley & Sons, Ltd.