For the Adams-Bashforth and Adams-Moulton methods of order four, a. Show that if / = 0, then F{thh, Wi+],w,+!_,) = 0. b. Show thatif /satisfies a Lipschitz condition with constant L, then a constant C exists with m h, Wi+U , w,+!_,) - F(ti, ll. Ui+I, . . . , Uj+lm) | \Wi+\-j - ul+|_;|.

l--r (-) ,ra: h,t J\ ) *l r-( { ,-. / 1 v cj*'Y L,: \ F l ,x€+ I 1- (- .I ,1 I \ '/t- *--':-- tI \ t/n 1"/ -tl t ('r \--i ,l-xr-lr-. *2 ' (k-!- \ \'j a'\-X u' V A. --) . -,\ -)"tI '