A routine approximates the solution to y′=x+y2 with y(0)=0 using a variable increment rule:
• Start with h1=0.20.
• After each accepted step, set the next increment hk+1=0.9hk if ∣f(xk,yk)∣>1, and hk+1=1.1hk otherwise, subject to 0.05≤hk+1≤0.30.
After two accepted steps the program reaches x2=0.42 with y2≈0.044. Which value will the program use for the third increment h3?
a) 0.18
b) 0.30
c) 0.24
d) 0.22