Najafi, Seyed Esmaeil SadatAllahviranloo, TofighAbbasbandy, SaeidMalkhalifeh, Mohsen Rostamy2025-04-172025-04-172025Najafi, S. E. S., Allahviranloo, T., Abbasbandy, S., & Malkhalifeh, M. R. (2025). Numerical solution of nonlinear equations of traffic flow density using spectral methods by filter. Journal of Applied Mathematics and Computing, 71(1), 743-763.1598-58651865-2085http://dx.doi.org/10.1007/s12190-024-02252-8https://hdl.handle.net/20.500.12713/6291This 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.eninfo:eu-repo/semantics/closedAccessEliminates ShockFilterSpectral MethodsTraffic FlowArticle711743763WOS:0013295104000032-s2.0-85205706715Q110.1007/s12190-024-02252-8Q1