A comparison of six numerical methods for integrating a compartmental Hodgkin-Huxley type model

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 explicit two implicit; three finite difference PDE methods, Runge-Kutta one an exponential time differencing method. Three first-, commonly considered second-, fourth-order. Derivations show, simulation data confirms, that Hodgkin-Huxley type cable equations render multiple order RK as first-order methods. Illustrations accuracy, stability, variations of action potential phase waveform statistics. Explicit were found unsuited for our given their inability to control consistency up 10μs less than the step size onset instability. While backward-time central space method performed satisfactorily first sizes 80μs, Hines-Crank-Nicolson method, only true second was unmatched 1−100μs.