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 $10\mathrm{\mu }\text{s}$ 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 $80\mathrm{\mu }\text{s}$, performance of the Hines-Crank-Nicolson method, our only true second order method, was unmatched for step sizes of $1-100\mathrm{\mu }\text{s}$.

我们在模拟常规尖峰皮层神经元模型时比较了六个数值积分器的性能，该模型的 74 个隔室配备了 11 个膜离子通道和钙动力学。四种方法是显式的，两种方法是隐式的；三种是有限差分 PDE 方法，两种是 Runge-Kutta 方法，一种是指数时间差分方法。三种方法是一阶方法，两种通常认为是二阶方法，一种是通常认为是四阶方法。推导表明，并且仿真数据证实，Hodgkin-Huxley 型电缆方程将多阶显式 RK 方法呈现为一阶方法。插图比较了准确性、稳定性、动作电位相位和波形统计的变化。发现显式方法不适合我们的模型，因为它们无法控制高达$10\mathrm{\mu }\text{秒}$小于开始不稳定的步长。虽然后向时间中心空间方法作为一阶方法表现令人满意，但步长可达$80\mathrm{\mu }\text{秒}$，我们唯一真正的二阶方法 Hines-Crank-Nicolson 方法的性能在步长为 $1-100\mathrm{\mu }\text{秒}$.