  Numerical computation of the time evolution of the mass transfer rate in a
close binary can be and, in particular, has been a computational challenge.
Using a simple physical model to calculate the mass transfer rate, we show that
for a simple explicit iteration scheme the mass transfer rate is numerically
unstable unless the time steps are sufficiently small. In general, more
sophisticated explicit algorithms do not provide any significant improvement
since this instability is a direct result of time discretization. For a typical
binary evolution, computation of the mass transfer rate as a smooth function of
time limits the maximum tolerable time step and thereby sets the minimum total
computational effort required for an evolutionary computation. By methods of
``Controlling Chaos'' it can be shown that a specific implicit iteration
scheme, based on Newton's method, is the most promising solution for the
problem.
