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 .
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