(30 points) Given the equation0u=f(u)with initial valueu(0) =u0and the numerical methodn+1nnu=u+ ??tf(u)(a) Define the local truncation error (LTE) for this method, and using Taylor expansions, determinewhat the order of the LTE is.(b) Define theglobal errorfor this method, and prove that the order of the method is the same asthe order of the LTE.0(c) If this method is applied to the problemu=-100uwith initial conditionu(0) = 1, for whatvalues of ??twill this method not blow up