The unique solution in the
antifunnel,
, has the value . (This is what a standard fourth-order Runge-Kutta
approximation will give if you solve backwards from t=-9,u=3 or from
; these points are on the top and the bottom of the
antifunnel, and thus should give upper and lower bounds for . An
error analysis done as in [4, chapter 3], and helped by the program
Numerical Methods from MacMath, shows that all written decimal
digits of are correct.) Thus a numerical solution of
, backward in time, starting with
, remains bounded for a
considerable length of time, as our computer experiments showed---but
eventually it will blow up, since the exact solution is
unstable as .