Question

2. f6pts) A proposed multistep method is given by Yn+1 = Yn + M(h) = Yn +h(Bifi + B3f3) where fk = f(yn-k, tn-k). Find Bk to maximize the order of the local error (minimize local error). Follow the example in the notes, define a = tn, F($) = f(y(s), s), rath I(h) = [** F(s) ds M(h) = h (B1F(a – h) + B3F(a – 3h)) eſh) = 1(h) – M(h) = E(0)h + E"(0)h² + (h) In the above eſh) is the local truncation error. Setting e'(0) = e" (0) = 0 yields two equations for Bk to be solved.

Answer 1

Solution that A proposed multistop method Griven given by is - Intl = 9n +M (h) = 96th CB, fi t Bafa) when fx = f cynkithak), we have to find Br. to marimize the order of the local erroa (minimize local euroa) now, we define with , frut) = fcy (u), ) - Ich) - puth Froder Mch) = hCB, F court) + By F (W-3h)) ech) -Sch) -MCH) = f'(o)h tys EMCORPECCA) the above ech) is the docal truncation In erado we equations to be set éco) = eco) to which yleeds two and from that two equations fre solved. // Hence proved above solution // ...... please upvote .....