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The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect

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  • Lei Yu
  • Bingchang Zhou

Abstract

A new continuum model with consideration of driver’s forecast effect is obtained to study the density wave problem and the stop‐and‐go phenomena. The stability condition of the new model is derived by using linear analysis. The triangular shock wave, one type of density wave, which is determined by Burgers equation in the stable region, is discussed in great detail with reductive perturbation method. The local cluster appears when we perform the numerical simulations for the new model. It also proves that the driver’s forecast effect has the positive effect of reducing the local cluster.

Suggested Citation

  • Lei Yu & Bingchang Zhou, 2014. "The Burgers Equation for a New Continuum Model with Consideration of Driver’s Forecast Effect," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:539459
    DOI: 10.1155/2014/539459
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    References listed on IDEAS

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