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The stiffness of the Hodgkin-Huxley (HH) equations during an action potential(spike) limits the use of large time steps. We observe that the neurons can beevolved independently between spikes, $i.e.,$ different neurons can be evolvedwith different methods and different time steps. This observation motivates usto design fast algorithms to raise efficiency. We present an adaptive method,an exponential time differencing (ETD) method and a library-based method todeal with the stiff period. All the methods can use time steps one order ofmagnitude larger than the regular Runge-Kutta methods to raise efficiency whileachieving precise statistical properties of the original HH neurons like thelargest Lyapunov exponent and mean firing rate. We point out that the ETD andlibrary methods can stably achieve maximum 8 and 10 times of speedup,respectively.

Design Fast Algorithms For Hodgkin-Huxley Neuronal Networks