  The Feynman integral is one of the most accurate methods for calculating
density operator dynamics in open quantum systems. However, the number of time
steps that can realistically be used is always limited, therefore one often
obtains an approximation of the density operator at a sparse grid of points in
time. Instead of relying only on \textit{ad hoc} interpolation methods such as
splines to estimate the system density operator in between these points, I
propose a method that uses physical information to assist with this
interpolation. This method is tested on a physically significant system, on
which its use allows important qualitative features of the density operator
dynamics to be captured with as little as 2 time steps in the Feynman integral.
This method allows for an enormous reduction in the amount of memory and CPU
time required for approximating density operator dynamics within a desired
accuracy. Since this method does not change the way the Feynman integral itself
is calculated, the value of the density operator approximation at the points in
time used to discretize the Feynamn integral will be the same whether or not
this method is used, but its approximation in between these points in time is
considerably improved by this method.
