It is known that, depending on the numerical method, the simulation accuracy of a spiking neuron increases monotonically and that the computational cost increases in a power-law complexity as the time step reduces. Moreover, the mechanism responsible for generating the action potentials also affects the accuracy and computational cost. However, little attention has been paid to how the time span and firing rate influence the simulation. This study describes how the time span and firing rate variables affect the accuracy, computational cost, and efficiency. It was found that the simulation is importantly affected by these two variables.