Solve PDE system with initial conditions

I need to solve

dUi(t,x)/dt+а*dUi(t,x)/dx=f(Ui(t,x),t,x), where i=1,...,4

system of PDE with initial conditions.

I tried pdepe, but it's obligatory to set boundary conditions. I have read about discretization method, but understood nothing.

Maybe there are another ways to solve this system?

Or maybe you will provide some examples for discretization method?

[Torsten]

Maybe a start:

Lee, Matthews: A Matlab method of lines template for transport equations