Rigorous pointwise approximations for invariant densities of non-uniformly 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∗⋅(lnm)/m, where C∗ is a computable fixed constant and m−1 is the mesh size of the discretization.