The initial-value problem

y' = e^y, 0≤ t ≤ 0.20, y(0) = 1

Has solution

y(t) = 1 − ln(1 − et).

Applying the three-step Adams-Moulton method to this problem is equivalent to finding the fixed point w_i+1 of

g(w) = w_i + h/24(9e^w + 19e^wi − 5e^wi−1 + e^wi−2 ) .

a. With h = 0.01, obtain w_i+1 by functional iteration for i = 2. . . 19 using exact starting values w₀,w₁, and w₂. At each step use w_i to initially approximate w_i+1.

b. Will Newton’s method speed the convergence over functional iteration?