Rigorous pointwise approximations for invariant densities of nonuniformly expanding maps

We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate $C^{\ast }\cdot \frac{\ln m}{m}$, where $C^{\ast }$ is a computable fixed constant and $m^{-1}$ is the mesh size of the discretization.