  We compare six numerical integrators' performance when simulating a regular
spiking cortical neuron model whose 74-compartments are equipped with eleven
membrane ion channels and Calcium dynamics. Four methods are explicit and two
are implicit; three are finite difference PDE methods, two are Runge-Kutta
methods, and one an exponential time differencing method. Three methods are
first-, two commonly considered second-, and one commonly considered
fourth-order. Derivations show, and simulation data confirms, that
Hodgkin-Huxley type cable equations render multiple order explicit RK methods
as first-order methods. Illustrations compare accuracy, stability, variations
of action potential phase and waveform statistics. Explicit methods were found
unsuited for our model given their inability to control spiking waveform
consistency up to 10 microseconds less than the step size for onset of
instability. While the backward-time central space method performed
satisfactorily as a first order method for step sizes up to 80 microseconds,
performance of the Hines-Crank-Nicolson method, our only true second order
method, was unmatched for step sizes of 1-100 microseconds.
