Abstract

In this research paper, we present a second order non-oscillatory central scheme. Our aim is to solve a non-local conservation law arising in traffic flow models with non-local mean velocity. The proposed scheme proves to be more accurate. It, in some way, resembles the Godunov-type scheme. Yet, it is better than the widely used Lax-Friedrich-type scheme. To prove our thesis, We conduct a series of numerical experiments in which we perform the following: A) We study and test the ratio of accuracy of our second-order scheme. B) We make clear and demonstrate the non-oscillatory character. C) We examine the convergence of the non-local solution to the local solution.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 4
Year: 2022

DOI: 10.12732/ijam.v35i4.2

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