The determination of periodic states of cyclic chemical processes by standard simulation techniques is computationally inefficient due to the long transient phase. We introduce the Newton-Picard method, a hybrid convergence acceleration method and compare its performance to the performance of existing convergence accelerating techniques. The comparison is made with respect to the number of function evaluations, robustness and dependence on initial conditions. We also discuss, depending on the characteristics of the chemical process, which acceleration method has the best performance.