1. Recall the test IVP y' = Ay and y(0) = a. We consider the so-called implicit Trapzoidal method h W4+1 = w + (f(t+1, W+1) + (tr, wr)) . to solve the test IVP which is a stiff system. (a) Write down the stability function Q(h) for the implicit Trapzoidal method (Hint: Q(h) is obtained by applying the implicit Trapzoidal method to the test IVP, see Lec 11, Theorem 1) (b) For the stability function, show that if h is a real number and h <0, we have |Q(h)| < 1. (c) (Optional) For the stability function, verify that for any h such that Re(h) < 0, we have Q(h) 1. (This shows the implicit trapezoidal method is A-stable.)