# Numerical Solution of a One-Dimensional Second Order Macroscopic Traffic Flow Model with a Source Term.

The study of traffic models has given rise to many models with the aim of realistically determining the behavior of traffic. The dynamics of the macroscopic traffic flow is modeled by a partial differential equation, where the object of study is to determine the density of traffic flow. We derived a second order macroscopic traffic flow model equation from a first order one using the Fick’s law of diffusion. We formulated second order macroscopic traffic flow model equation with a source term, and solved numerically using explicit forward finite difference method. The results obtained from the numerical example using MATLAB show that the traffic density continues to decrease as the traffic moves along a stretch of road at time . These results were discussed and illustrated graphically for easy visualization.

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APA

Ojike, E. & Aboiyar, T (2018). Numerical Solution of a One-Dimensional Second Order Macroscopic Traffic Flow Model with a Source Term.. Afribary. Retrieved from https://afribary.com/works/numerical-solution-of-a-one-dimensional-second-order-macroscopic-traffic-flow-model-with-a-source-term

MLA 8th

Ojike, Emmanuel, and Terhemen Aboiyar "Numerical Solution of a One-Dimensional Second Order Macroscopic Traffic Flow Model with a Source Term." Afribary. Afribary, 21 Nov. 2018, https://afribary.com/works/numerical-solution-of-a-one-dimensional-second-order-macroscopic-traffic-flow-model-with-a-source-term. Accessed 21 Jun. 2024.

MLA7

Ojike, Emmanuel, and Terhemen Aboiyar . "Numerical Solution of a One-Dimensional Second Order Macroscopic Traffic Flow Model with a Source Term.". Afribary, Afribary, 21 Nov. 2018. Web. 21 Jun. 2024. < https://afribary.com/works/numerical-solution-of-a-one-dimensional-second-order-macroscopic-traffic-flow-model-with-a-source-term >.

Chicago

Ojike, Emmanuel and Aboiyar, Terhemen . "Numerical Solution of a One-Dimensional Second Order Macroscopic Traffic Flow Model with a Source Term." Afribary (2018). Accessed June 21, 2024. https://afribary.com/works/numerical-solution-of-a-one-dimensional-second-order-macroscopic-traffic-flow-model-with-a-source-term

##### Document Details
Field: Industrial Mathematics Type: Paper 8 PAGES (3052 WORDS) (pdf)