Solved: Consider the initial-value problem y 2y, y(0) 1. The analytic solution is y(x)
Chapter 6, Problem 16(choose chapter or problem)
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 fourth-order RK4 method.
(b) Find a bound for the local truncation error in \(y_{1}\).
(c) Compare the actual error in \(y_{1}\) 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(\(h^{4}\)) by comparing the errors in parts (a) and (d).
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