Example 5.  Show that the degree of precision of  Simpson’s Rule is  [Graphics:Images/NewtonCotesMod_gr_194.gif].  

Solution 5.

It will suffice to apply Simpson’s Rule over the interval  [0,2]  with the five test functions  [Graphics:../Images/NewtonCotesMod_gr_195.gif].

[Graphics:../Images/NewtonCotesMod_gr_196.gif]
[Graphics:../Images/NewtonCotesMod_gr_197.gif]
[Graphics:../Images/NewtonCotesMod_gr_198.gif]

The function  [Graphics:../Images/NewtonCotesMod_gr_199.gif]  is the lowest power of  x  for which the Simpson’s rule is not exact.

 

[Graphics:../Images/NewtonCotesMod_gr_200.gif]


[Graphics:../Images/NewtonCotesMod_gr_201.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004