Online dynamic security assessment involves analyzing the effect of a large number of contingencies in a short time. This is a computationally demanding task, and use of energy function method reduces the computational burden. Energy function method involves determination of a quantity called critical energy which requires system simulation for a short duration. In spite of the use of energy function method, there is a significant computational requirement since a large number of contingencies have to be analyzed. In this paper, a comparison of the performance, in terms of accuracy and speed, of different numerical methods in the determination of critical energy, is presented. © 2015 IEEE.