Solver for first-order PDE in 1D

Hello everybody,

I have a problem solving a first order nonlinear system of PDE in 1D. The pdepe seemed to be a good tool for 1D but it only works for second order systems.

Is their a tool for first order PDE in 1D?

Thanks

NB

PS: The system would be something like

du1/dt + d((u1-u2)/u1)/dt = (u1-u2)^2

du1/dt + d((u2-u1)/u2)/dt = -(u1-u2)^2

BC: u1 = u2 in both borders (0 and 1 for instance if the domain is [0,1]

PPS: Is there a way to put periodic boundary conditions in the different Matlab solvers?