Consider the initial-value problem y’ = 2x – 3y + 1, y(1) = 5. The analytic solution is
(a) Find a formula involving c and h for the local truncation error in the nth step if Euler’s method is used.
(b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5).
(c) Approximate y(1.5) using h = 0.1 and h = 0.05 with Euler’s method. See Problem 1 in Exercises 2.6.
(d) Calculate the errors in part (c) and verify that the global truncation error of Euler’s method is O(h).
