Illustrative Examples
Example 1: If and , we get
Hence , which gives the second order Adams-Bashforth method
or
If, on the other hand, is given, there exists a of degree K such that the method is of order We find this by dividing (8.8) by log to get
.
Since is analytic at must be analytic at if , that is,
Example 2: If we get
Hence, , which gives the third order Adams-Moulton method:
and 
, we get 
, which gives the second order Adams-Bashforth method 
is given, there exists a 
of degree K such that the method is of order 
We find this by dividing (8.8) by log 
to get 
. 
is analytic at 
must be analytic at 
if 
, that is, 
we get 
, which gives the third order Adams-Moulton method: 
