Exercise 5 (25 marks). Let a and S be real numbers and consider the following numerical method to approximate the solutions to the IVP y' = f(y) with initial condition y(0) = yo: starting from yo, for all n 2 0 define yn+1 by 2h Un+1 = yn + f(yn) (first predictor) h Un+1 = yn + col : f ( yn ) (second predictor) Un+1 = Un th [of (Un+1) + Bf (Un+1)] (corrector). 1. [10 marks] The quantities yn+1 and yn$ 1 predict the values of the solution y at certain points in the interval [In, In + h]. Which ones? Justify your answer. 2. 5 marks] Find a function (y, h) such that the method can be written yn+1 = Un + ho (yn, h). 3. [10 marks] We assume that f is indefinitely differentiable with continuous derivatives. For which conditions of a and S has the method a truncation error of order 1? Of order 2