Derive a global error bound for the numerical method h 2h y+1 = y;- + fC$iyl + f($a+1ay+1) for solving the differential equation 3/ = f(5c, 3;). You may assume f is Lipschitz (L) in the 3; variable, Hy\" | |Do S M, and we are interested in obtaining a numerical solution over the interval [(1,1)], where the initial condition is 3/(330) = yo, and 330 = a. N E N is the 1 number of panels and h = (b a)/N is the panel Width.You may also assume hL S 5 Your global error bound should be in the form ahM . _ . 0. Consider the problem of solving the differential equation y' = cos(y) + :c sin(y) 11(0) = 1 over [0, 1] using the method in the previous problem, h 2h y+1 = 311+ f(m1yi) + Efcrzrla @1341) Use your answer from the previous problem to nd an h > 0 value that ensures a global error of less than 103