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Journal of Information and Optimization Sciences

(Since 1980)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

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Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

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Journal of Information and Optimization Sciences
Open Access Research Article

Numerical solution of nonlinear equations of traffic flow density using filter methods with middle-grid point

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pp. 1461–1478Vol. 47Issue 4April 2026DOI: 10.47974/JIOS-1944XML
Received:
06 Aug 2024
Published Online:
11 Sep 2025
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

Spectral methodsMoving mesh methodTraffic flowMiddle-grid pointCentral-upwind schemes method

Subject Classifications

65M3035L0335L20

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