Apply the Improved Euler Method to the equation y' = y, y(0) = 1, with h =

Question:

Apply the Improved Euler Method to the equation y' = y, y(0) = 1, with h = 0.2, 0.1, 0.05, 0.01, 0.005 to approximate the solution on the interval [0,1]. Compute the error in approximating y(1) and fill in the following table. For the Improved Euler Method, is the error proportional to h, h2, or some other power of h?