Suppose y solves the initial value problem y(1)=1, y′(t)=2t for t>1. Explain why the RK2 method should compute the exact solution. Use this fact to give an expression for α in terms of b.
I'm going back through old exam papers in preparation for my finals and I would love some help on this particular question.
The RK2 method is an order 2 method and thus exact in the integration of polynomials in $t$ up to degree 1. Depending on what the RK2 method actually is, the reduction to the integration of functions in $t$ is either the midpoint or the trapezoidal summation method, which again are exact on linear functions.
