Repeat Problem 16 using the initial-value problem y’ = -2y

Repeat Problem 16 using the initial-value problem y’ = -2y + x, y(0) = 1. The analytic solution is

Problem 16

Consider the initial-value problem y’ = 2y, y(0) = 1. The analytic solution is y(x) = e^2x.

(a) Approximate y(0.1) using one step and the RK4 method.

(b) Find a bound for the local truncation error in y1.

(c) Compare the error in y1 with your error bound.

(d) Approximate y(0.1) using two steps and the RK4 method.

(e) Verify that the global truncation error for the RK4 method is O(h⁴) by comparing the errors in parts (a) and (d).