Before revision:  For pulse-coupled HH networks, the synaptic spike times are unknown before evolving. We have to evolve the network without considering them and carefully assign them at the end of time step to achieve a second-order accuracy. We find that the second-order ETD method with Runge-Kutta time stepping (ETD2RK) is less accurate than the second-order Runge-Kutta method (RK2) using a common time step. Besides, we observe that the HH equations are quite flat outside the stiff period where RK2 method also allows a large time step.
After revision:  For pulse-coupled HH networks, the synaptic spike times cannot be predetermined and are convoluted with neuron's trajectory itself. This presents a challenging issue for the design of an efficient numerical simulation algorithm. The stiffness in the HH equations are quite flat outside the stiff period where RK2 method also allows a large time step.