The Exact Solution of Burgers’ Equation in Traffic Flow

Sim, Ka Yee (2022) The Exact Solution of Burgers’ Equation in Traffic Flow. Final Year Project (Bachelor), Tunku Abdul Rahman University College.

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Abstract

The Burgers' equation is a nonlinear partial differential equation used in the applied mathematics field, including fluid mechanism, gas dynamics, and traffic flow. In this project, the Burgers' equation will be used to model a simple traffic flow problem, assuming one traffic light on the single-lane road. The analytic solution of the viscid one-dimensional Burgers’ equation in solving the traffic problem is the focus of this project. It will be derived using the Cole-Hopf Transformation method, subject to the initial value problem. Then, a heat equation is expected to be obtained, and the method of separable variable is used as the solver for the heat equation. As the analytic solution has been obtained, the effect on changing parameters to the graph is observed and interpreted. MAPLE computer programming which is user-friendly will be used to produce various graphical outputs to simulate the propagation of solitons. The viscosity term that appears in traffic flow will be interpreted with the appropriate graphing incorporating with the real-life explanation.