The eigen‐structure of the Jacobian in multi‐class Lighthill‐Whitham‐Richards traffic flow models

Abstract

AbstractCharacteristic‐based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen‐decomposition of the Jacobian matrix of the system. For the Multi‐Class Lighthill‐Witham‐Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen‐vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)