In this thesis, we implement Euler's method and the Runge-Kutta method to solve initial value problems. A goal of the project is to compare the two methods on preliminary problems illustrating limitations and advantages. We also apply the Runge-Kutta method to a mathematical model of traffic flow. This thesis sheds light on how the fourth-order Runge-Kutta method is implemented to solve the Optimal Velocity Model (Kurata & Nagatani, 2003). We identify initial conditions and base cases to run simulations of the model. We consider one-car and two-car systems to validate the application of the fourth-order Runge-Kutta method and the Optimal Velocity Model. Our simulations accurately capture practical traffic scenarios.
Laura K. Gross (Thesis Director)
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Original document was submitted as an Honors Program requirement. Copyright is held by the author.
Mullen, Terry. (2015). An Analysis of Numerical Methods on Traffic Flow Models. In BSU Honors Program Theses and Projects. Item 105. Available at: https://vc.bridgew.edu/honors_proj/105
Copyright © 2015 Terry Mullen