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 the RK4 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 the RK4 method with h = 0.1 and h [1] 0.05. See Problem 3. You will need to carry more than six decimal places to see the effect of reducing the step size.

Transcribed Image Text:

38 -3(x-1)