The model equation of simulated moving bed (SMB) process is solved by a space-time conservation element and solution element (CE/SE) method, which is found to be more efficient than other methods in the two case studies. Furthermore, this CE/SE method was combined with continuous prediction technique (CPM) to further accelerate determination of the cyclic steady state in SMB operation. Comparing with conventional method of lines at the same required precisions, CE/SE with CPM was proved to save the CPU time by 77% for the pseudo-linear system of glucose-fructose separation and 96% for nonlinear enantioseparation. Finally, the combination of CE/SE and CPM was applied to the optimization study to determine the optimum switching time and flow rate. To ensure the method be convergent, the four Courant numbers in four zones need to fall between 0.1 and 1. The method for fulfill this constraint is also developed. (C) 2015 Elsevier B.V. All rights reserved.