Problem 6. (10 points) Consider the initial value ODE problem y' = f(y) with y(to) = yo and suppose all the derivatives of f are continuous. Let tk = to + kh where h (0,1). Consider the implicit method given by Yk+2 = ayk + byk+1 + chf (yk+2). The local truncation error (LTE) for this implicit method is LTE of implicit := |y(t2) - y2= y(+2) [ay(to) +by(t1)+chf(y(t2))]]. Determine the coefficients a, b, and c that give the highest order LTE for this method. What is the order for this method? Hint: Approximate y(ti) and y(to) using the Taylor approximation of y about t2. Problem 6. (10 points) Consider the initial value ODE problem y' = f(y) with y(to) = yo and suppose all the derivatives of f are continuous. Let tk = to + kh where h (0,1). Consider the implicit method given by Yk+2 = ayk + byk+1 + chf (yk+2). The local truncation error (LTE) for this implicit method is LTE of implicit := |y(t2) - y2= y(+2) [ay(to) +by(t1)+chf(y(t2))]]. Determine the coefficients a, b, and c that give the highest order LTE for this method. What is the order for this method? Hint: Approximate y(ti) and y(to) using the Taylor approximation of y about t2