We present a numerical simulation algorithm that is well suited for the study of noise-induced transport processes. The algorithm has two advantages over standard techniques: ( 1 ) it preserves the property of detailed balance for systems in equilibrium and (2) it provides an efficient method for calculating nonequilibrium currents. Numerical results are compared with exact solutions from two different types of correlation ratchets, and are used to verify the results of perturbation calculations done on a three-state ratchet.