Example 6.  Show that the degree of precision of  Simpson’s [Graphics:Images/NewtonCotesMod_gr_202.gif] Rule is  [Graphics:Images/NewtonCotesMod_gr_203.gif].  

Solution 6.

It will suffice to apply Simpson’s [Graphics:../Images/NewtonCotesMod_gr_204.gif] Rule over the interval  [0,3]  with the five test functions  [Graphics:../Images/NewtonCotesMod_gr_205.gif].

[Graphics:../Images/NewtonCotesMod_gr_206.gif]
[Graphics:../Images/NewtonCotesMod_gr_207.gif]
[Graphics:../Images/NewtonCotesMod_gr_208.gif]

The function  [Graphics:../Images/NewtonCotesMod_gr_209.gif]  is the lowest power of  x  for which the Simpson’s [Graphics:../Images/NewtonCotesMod_gr_210.gif] rule is not exact.

 

[Graphics:../Images/NewtonCotesMod_gr_211.gif]


[Graphics:../Images/NewtonCotesMod_gr_212.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004