2. Three-step Adams-Bashforth method Consider the interpolation nodes {t-2, ti-1, t} where t = tij + jh. (a) Write down the Lagrange interpolation polynomial P(t) for the function f(t, y(t)) at the nodes above. (b) Consider the IVP y'(t) = f(t, y(t)), integrate the Lagrange polynomial P(t) from (a) exactly to determine b, b and by such that Yi+1 - Y h (bf (t, y) + bf (ti-1: Yi-1)+b3f(ti-2: Yi-2)), As usual, y denotes the value of y(t) at t = tk. Your answers by should be given as fractions. (Hint: you may note for b, we have 1 hb = Li (t) dt = = (t-ti-1)(t-ti-2) dt, 2h2 evaluate the integral and do the same for b, b3.)