Compare the results of i to the exact solution and comment

Question

Use 4^th order AB-AM-predictor-corrector method to obtain the solution of the following initial value problem:

dy/dt = (-2t + y)² - 7, y(0) = 0

i) Use a step size of h=0.1, h=0.05 and h=0.01 to find the approximate solutions on the interval 0 ≤ t ≤ 1;

ii) Given the analytic solution y = 2t + 3(1-e^6t)/1-e^6t, Compare the results of i) to the exact solution and comment on the accuracy of the numerical algorithm and adopted step size.