Change Algorithm 5.4 so that the corrector can be iterated for a given number p iterations. Repeat Exercise 7 with p = 2, 3, and 4 iterations. Which choice of p gives the best answer for each initial-value problem?

In Exercise 7

a. y' = y/t − (y/t)², 1≤ t ≤ 2, y(1) = 1, with h = 0.1; actual solution y(t) = t/(1 + ln t).

b. y' = 1+y/t+(y/t)², 1≤ t ≤ 3, y(1) = 0, with h = 0.2; actual solution y(t) = t tan(ln t).

c. y' = −(y + 1)(y + 3), 0 ≤ t ≤ 2, y(0) = −2, with h = 0.1; actual solution y(t) = −3 + 2/(1 + e^−2t).

d. y' = −5y+5t²+2t, 0≤ t ≤ 1, y(0) = 1/3, with h = 0.1; actual solution y(t) = t²+1/3 e^−5t .