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It is well known that for different classes of transformations, including the class of piecewise C 2 expanding maps T : [0, 1] , Ulam's method is an efficient way to numerically approximate the absolutely continuous invariant measure of T . We develop a new extension of Ulam's method and prove that this extension can be used for the numerical approximation of the Ruelle-Perron-Frobenius operator associated with T and the potential φ β = −β log |T |, where β ∈ R. In particular, we prove that ourdoi:10.1088/0951-7715/21/9/001 fatcat:epsbpuschfg3xiztdk4qip34xe