= = =

C2 (X = 1, and f3 = I, which yields the modified Euler FDEs. Thus,

I I h Yn+' =Yn +:2 I1YI +:2 I1Y2 =Yn +2U;' +/"+1)

(7.170) (7.171)

(7.172)

Letting C, = 0 gives C2 = 1, (X = ~, and {J = ~, which yields the modified midpoint FDEs. Thus,

( h I1Y ,) .