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Formulation of a maximum principle satisfying a numerical scheme for traffic flow models. (English) Zbl 1452.65156

Summary: We consider a non-local traffic flow model with Arrhenius look-ahead dynamics. In recent times, a maximum principle satisfying local conservation framework has been getting much attention, yet conventional numerical approximation scheme may lead to a breakdown of the maximum principle. In this paper, we construct a maximum principle satisfying a numerical scheme for a class of non-local conservation laws and present numerical simulations for the traffic flow models. The technique and the idea developed in this work are applicable to a large class of non-local conservation laws.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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