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  • Küçük Resim
    Öğe
    Numerical solution of nonlinear equations of traffic flow density using spectral methods by filter
    (Springer nature, 2025) Najafi, Seyed Esmaeil Sadat; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This paper introduces an innovative approach that marries the spectral method with a time-dependent partial differential equation filter to tackle the phenomenon of shock waves in traffic flow modeling. Through the strategic application of Discrete low-pass filters, this method effectively mitigates shock-induced deviations, leading to significantly more accurate results compared to conventional spectral techniques. We conduct a thorough examination of the stability conditions inherent to this approach, providing valuable insights into its robustness. To substantiate its effectiveness, we present a series of numerical examples illustrating the method's prowess in delivering precise solutions. Comparative analysis against established methods such as Lax and Cu reveals a marked superiority in accuracy. This work not only contributes a novel numerical technique to the field of traffic flow modeling but also addresses a persistent challenge, offering a promising avenue for further research and practical applications.
  • Küçük Resim
    Öğe
    Numerical solution of nonlinear equations of traffic flow density using spectral methods by filter
    (Springer nature, 2025) Najafi, Seyed Esmaeil Sadat; Allahviranloo, Tofigh; Abbasbandy, Saeid; Malkhalifeh, Mohsen Rostamy
    This paper introduces an innovative approach that marries the spectral method with a time-dependent partial differential equation filter to tackle the phenomenon of shock waves in traffic flow modeling. Through the strategic application of Discrete low-pass filters, this method effectively mitigates shock-induced deviations, leading to significantly more accurate results compared to conventional spectral techniques. We conduct a thorough examination of the stability conditions inherent to this approach, providing valuable insights into its robustness. To substantiate its effectiveness, we present a series of numerical examples illustrating the method's prowess in delivering precise solutions. Comparative analysis against established methods such as Lax and Cu reveals a marked superiority in accuracy. This work not only contributes a novel numerical technique to the field of traffic flow modeling but also addresses a persistent challenge, offering a promising avenue for further research and practical applications.