  We consider a pair of stochastic integrate and fire neurons receiving
correlated stochastic inputs. The evolution of this system can be described by
the corresponding Fokker-Planck equation with non-trivial boundary conditions
resulting from the refractory period and firing threshold. We propose a finite
volume method that is orders of magnitude faster than the Monte Carlo methods
traditionally used to model such systems. The resulting numerical
approximations are proved to be accurate, nonnegative and integrate to 1. We
also approximate the transient evolution of the system using an
Ornstein--Uhlenbeck process, and use the result to examine the properties of
the joint output of cell pairs. The results suggests that the joint output of a
cell pair is most sensitive to changes in input variance, and less sensitive to
changes in input mean and correlation.
