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Mathematics > Numerical Analysis

arXiv:2311.04306 (math)
[Submitted on 7 Nov 2023 (v1), last revised 11 Nov 2023 (this version, v2)]

Title:High-Order Numerical Method for 1D Non-local Diffusive Equation

Authors:D. Do, H. Nick Zinat Matin, M. L. Delle Monache
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Abstract:In this paper we present a non-local numerical scheme based on the Local Discontinuous Galerkin method for a non-local diffusive partial differential equation with application to traffic flow. In this model, the velocity is determined by both the average of the traffic density as well as the changes in the traffic density at a neighborhood of each point. We discuss nonphysical behaviors that can arise when including diffusion, and our measures to prevent them in our model. The numerical results suggest that this is an accurate method for solving this type of equation and that the model can capture desired traffic flow behavior. We show that computation of the non-local convolution results in $\mathcal{O}(n^2)$ complexity, but the increased computation time can be mitigated with high-order schemes like the one proposed.
Comments: 17 pages and 8 figures
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2311.04306 [math.NA]
  (or arXiv:2311.04306v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2311.04306

Submission history

From: Hossein Nick Zinat Matin [view email]
[v1] Tue, 7 Nov 2023 19:24:24 UTC (2,135 KB)
[v2] Sat, 11 Nov 2023 09:51:56 UTC (2,135 KB)
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