NUMERICAL RESULTS FOR THE IVP TO THE BURGER'S EQUATION WITH EXTERNAL FORCES
Crystal Mackey1, Alejandra Castillo2, Armando Morales3, Julio César Enciso Alva4, Cynthia Flores3.
1Youngstown State University, Youngstown, OH, 2Pomona College, Claremont, CA, 3California State University, Channel Islands, Camarillo, CA, 4Universidad Autónoma del Estado de Hidalgo, Pachuca, Hidalgo, MX.
In this project, we use Burger's equation to study traffic flow, including shock and rarefaction waves, where traffic density, traffic flow, and velocity are the main variables expressed as functions of position and time. The derivation of the conservation law from physical principles can be reduced to Burger's equation. The initial value problem (IVP) of Burger's equation is a partial differential equation with an initial condition. Our objective is to numerically approximate solutions to the IVP for Burger's equation with external forces. After deriving the Lax-Wendroff method and modifying it to improve numerical approximations, adaptations were made to include an external force term. External forces may help to capture physical traffic interpretations such as traffic lights, driver interactions, multiple lanes, or on and off ramps on a highway. Our goal is to approximate solutions to the IVP for Burger's equation with external forces and compare our numerical simulations to real data. In this poster, we compare our numerical simulations to real data and present the methods used.