  Waveform-relaxation methods divide systems of differential equations into
subsystems and therefore allow for parallelization across the system. Here we
present an application for ODE waveform-relaxation methods in the context of
spiking neural network simulators. Parallel spiking neural network simulators
make use of the fact that the dynamics of neurons with chemical synapses is
decoupled for the duration of the minimal network delay and thus can be solved
independently for this duration. The inclusion of electrical synapses,
so-called gap junctions, requires continuous interaction between neurons and
therefore constitutes a conceptional problem for those simulators. We present a
suitable waveform-relaxation method for an efficient integration of gap
junctions and demonstrate that the use of the waveform-relaxation method
improves both, accuracy and performance, compared to a non-iterative solution
of the problem. We investigate the employed method in a reference
implementation in the parallel spiking neural network simulator NEST.
