Another comparison we have carried out concerns a chaotic ¶ section computed
by both methods. Using the same initial condition and A = 13 in both cases, we
calculated 
to 
. We have plotted only the
first 100 values in figure 6 for clarity. Note that the actual point
positions calculated by both methods diverge from each other (only to be
expected in a chaotic system), but that the underlying structure of the attractor
is insensitive to the method of calculation.
As an aside, it is interesting to note that our approximation runs about 45 times faster than the standard numerical method.
Figure: Comparison of ¶ sections for A = 13.