1. (30 points) Given the equation w' = f(u) with initial value (0) = ug and the numerical method wtl = u" + At f(u) (a) Define the local truncation error (LTE) for this method, and using Taylor expansions, determine what the order of the LTE is. (b) Define the global error for this method, and prove that the order of the method is the same as the order of the LTE. () If this method is applied to the problem " = 100u with initial condition u(0) = 1, for what values of At will this method not blow up