Dynamic security assessment (DSA) examines whether the power system is stable under large disturbances. There is a time constraint for online analysis since it has to be performed for a large number of contingencies in every few tens of minutes. In order to reduce the amount of computation, screening is performed to identify those contingencies which are sure to not cause system instability and hence can be eliminated; the other contingencies have to be scrutinized further. The computation required is in the numerical solution of differential equations. The amount of computation depends on step size; but increase in step size results in larger errors. This paper proposes a measure of local error in the numerical solution. Case studies are conducted on 10 generator New England system and 17 generator IEEE test system. Runge-Kutta explicit and implicit methods with different step sizes and tolerances are compared based on the proposed measure of error. Hence the most accurate numerical method satisfying the time constraint can be chosen for online DSA. © 2013 IEEE.