The problem: You are given the problem of analyzing the dynamics of a line of cars moving on a one-lane highway. One approach to this problem is to assume that the line of cars behaves like a group of coupled oscillators. How would you set this problem up in a tractable way? Make lots of assumptions. Can anyone help me get started on this? I'm having trouble even setting up the differential equation.
There is a write-up on traffic flow using first order PDEs in "Basic Partial Differential Equations" by Bleecker and Csordas. Try and find it in the library. This is the equation that is derived: [tex]\rho_t+M(1-2\frac{\rho}{d})\rho_x=0[/tex] Although maybe you're looking for just an ODE model.