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?

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

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