  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 be
evolved independently between spikes, $i.e.,$ different neurons can be evolved
with different methods and different time steps. This observation motivates us
to design fast algorithms to raise efficiency. We present an adaptive method,
an exponential time differencing (ETD) method and a library-based method to
deal with the stiff period. All the methods can use time steps one order of
magnitude larger than the regular Runge-Kutta methods to raise efficiency while
achieving precise statistical properties of the original HH neurons like the
largest Lyapunov exponent and mean firing rate. We point out that the ETD and
library methods can stably achieve maximum 8 and 10 times of speedup,
respectively.
