  We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the
Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase
transition in the directed percolation universality class. Estimates for the
stochastic time evolution, phase boundaries and critical exponents can be
obtained with high precision. This is possible using only modest numerical
effort since the thermodynamic limit can be taken analytically in our approach.
We also point out further advantages of the TMRG over other numerical
approaches, such as classical DMRG or Monte-Carlo simulations.
