For y′=x2−y a program is currently at the point (0.5,0.3) with increment h=0.20. It computes a tentative next point (x∗,y∗)=(0.7,0.29) and an error estimate
E^=21h∣f(x∗,y∗)−f(x0,y0)∣.
If E^>0.01 the step is rejected and h is halved; if E^<0.002 the step is accepted and the next h is doubled (capped at 0.30); otherwise the step is accepted with h unchanged. Which of the following describes the correct outcome for this step?
a) Step accepted; next increment h=0.30.
b) Step accepted; next increment h=0.20.
c) Step rejected; next increment h=0.10.
d) Step rejected; next increment h=0.05.