Open Access
Research Article
Numerical solution of nonlinear equations of traffic flow density using filter methods with middle-grid point
Seyed Esmaeil Sadat Najafiseyedesmaeilsadatnajafi@gmail.comDepartment of Mathematics Science and Research Branch Islamic Azad UniversityTehran, 1477893855, IranView full profile → , Tofigh Allahviranlootofigh.allahviranloo@eng.bau.edu.tr; allahviranloo@gmail.comDepartment of Mathematics Science and Research Branch Islamic Azad University; Faculty of Engineering and Natural Sciences Istinye UniversityDepartment of Mathematics Science and Research Branch Islamic Azad UniversityTehran, 1477893855, IranView full profile → , *Saeid AbbasbandyCorresponding authorabbasbandy@sci.ikiu.ac.ir; abbasbandy@yahoo.comDepartment of Applied Mathematics Faculty of Science Imam Khomeini International UniversityQazvin, 3414916818, IranView full profile → , Mohsen Rostamy Malkhalifehmohsenrostamy@yahoo.comDepartment of Mathematics Science and Research Branch Islamic Azad UniversityTehran, 1477893855, IranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 06 Aug 2024
- Published Online:
- 01 Apr 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1944
- Pages:
- 1461–1478
Abstract
This study addresses the significant challenge of accurately simulating traffic flow in heavily congested urban areas through microscopic traffic models. These models employ differential equations to simulate the behavior of individual vehicles, providing valuable insights into traffic patterns and congestion levels. However, conventional numerical techniques, such as the spectral method, often fall short of accurately capturing traffic dynamics, resulting in the introduction of shocks that cause substantial inaccuracies. To overcome this problem, we propose a novel method that incorporates a Discrete Singular Convolution (DSC) filter. This innovative approach effectively manages and reduces shocks during numerical simulations by adaptively combining discrete convolution filters, thus achieving higher accuracy and computational efficiency. Our method significantly minimizes errors in comparison to traditional techniques. We validate our proposed method by applying it For the Lighthill–Whitham–Richards traffic flow model through a series of numerical experiments. The results demonstrate the superior performance of our approach over traditional schemes, such as Lax and Friedrichs. We compare our findings with the analytical solutions of the relevant equations, showcasing the potential of our method to enhance the accuracy of traffic flow modeling. This improvement has promising implications for traffic management and urban planning.
Keywords
Subject Classifications
65M3035L0335L20
References
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