Spiking neurons are described using ordinary differential equations and are commonly solved using Euler's method. An important factor that has a significant impact on the performance and cost of spiking neurons simulation and yet its importance has been neglected in the published literature, is the time step in Euler's method. In this paper, it was uncovered that the threshold time step that Izhikevich neuron becomes unstable is an exponential function of the input current. Software simulation performance were compared for different time steps. Afterwards, the model implemented on the FPGA. Hardware performance metrics were measured for each time step. Results indicated that by determining maximum input current to the neuron, larger time steps comparable to that used in the previous works could be employed.