Consider the following two-stage Runge-Kutta method U^(n+1) = U^n + k(1/4F0 + 3/4 F1) with F0 = f(U^n,tn) F1 = f(U^n + 2/3kF0, tn + 2/3 k) (a). Show...

Consider the following two-stage Runge-Kutta method

U^(n+1) = U^n + k(1/4F0 + 3/4 F1)

with F0 = f(U^n,tn)

F1 = f(U^n + 2/3kF0, tn + 2/3 k)

(a). Show the local truncation error is O(k 2 ).

(b). Show the global error is O(k 2 ).