This paper presents a comparison of computational algorithms to simulate action potentials using stochastic sodium channels. Four algorithms are compared in single-node models: Strassberg and DeFelice (1993) (SD), Rubinstein (1995) (R), Chow and White (1996) (CW), and Fox (1997) (F). Neural responses are simulated to a simple and a preconditioned monophasic current pulse. Three exact algorithms implementing Markov jumping processes (SD, R, CW) resulted in similar responses, while the approximation algorithm using Langevin's equation (F) showed quite different responses from those in the exact algorithms. The computational time was measured as well: 1(F), 7(CW), 32(SD), 39(R) relative to that of the F algorithm. Furthermore, it is shown that as the sampling step for integration of the transmembrane potential increases, neural responses in all algorithms tended to be different from those in dense sampling steps, however, the CW algorithm was robust even at a sparse sampling step. It is concluded that the most computationally efficient algorithm having appropriate properties of neural excitability is the CW algorithm.