6533b873fe1ef96bd12d54db
RESEARCH PRODUCT
The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models
P. MuletR. Donatsubject
Microscopic traffic flow modelConservation lawClass (set theory)symbols.namesakeJacobian matrix and determinantCalculusStructure (category theory)symbolsApplied mathematicsHyperbolic systemsEigenvalues and eigenvectorsMathematicsShock (mechanics)description
Characteristic-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)
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-12-01 | PAMM |