Seyed Esmaeil Sadat Najafi

Dissertation: This thesis 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