Euler’s Method Accuracy and Step Size Impact
Consider the second order differential equation \(y” = -y\) with initial conditions \(y(0)=1\) and \(y'(0)=0\). Convert this equation into a system of first order equations and use Euler’s method to approximate \(y(0.1)\) using two different step sizes: \(h=0.1\) and \(h=0.05\). Briefly explain which approximation is more accurate and why.