Formulation of a maximum principle satisfying a numerical scheme for traffic flow models

Oluwaseun Farotimi and Kuppalapalle Vajravelu ()
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Oluwaseun Farotimi: University of Central Florida
Kuppalapalle Vajravelu: University of Central Florida

Partial Differential Equations and Applications, 2020, vol. 1, issue 4, 1-11

Abstract: Abstract 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.

Keywords: Nonlocal conservation law; Traffic flow; Maximum principle; Numerical scheme; Primary 65M06; Secondary 35L65 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00022-2

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