For a program is currently at the point with increment

MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations

Problem

For y′=x2−yy'=x^{2}-y a program is currently at the point (0.5,0.3)(0.5,0.3) with increment h=0.20h=0.20. It computes a tentative next point (x∗,y∗)=(0.7,0.29)(x_{*},y_{*})=(0.7,0.29) and an error estimate E^=12h ∣f(x∗,y∗)−f(x0,y0)∣.\hat E=\tfrac12 h\,|f(x_{*},y_{*})-f(x_{0},y_{0})|. If E^>0.01\hat E>0.01 the step is rejected and hh is halved; if E^<0.002\hat E<0.002 the step is accepted and the next hh is doubled (capped at 0.300.30); otherwise the step is accepted with hh unchanged. Which of the following describes the correct outcome for this step? (a) Step accepted; next increment h=0.30h=0.30. (b) Step accepted; next increment h=0.20h=0.20. (c) Step rejected; next increment h=0.10h=0.10. (d) Step rejected; next increment h=0.05h=0.05.

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