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

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Listed:
  • Oluwaseun Farotimi

    (University of Central Florida)

  • Kuppalapalle Vajravelu

    (University of Central Florida)

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.

Suggested Citation

  • Oluwaseun Farotimi & Kuppalapalle Vajravelu, 2020. "Formulation of a maximum principle satisfying a numerical scheme for traffic flow models," Partial Differential Equations and Applications, Springer, vol. 1(4), pages 1-11, August.
    • Handle: RePEc:spr:pardea:v:1:y:2020:i:4:d:10.1007_s42985-020-00022-2
    DOI: 10.1007/s42985-020-00022-2
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    References listed on IDEAS

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    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
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