Example 10.  When the step size is reduced by a factor of [Graphics:Images/SimpsonRuleMod_gr_176.gif] the error term  [Graphics:Images/SimpsonRuleMod_gr_177.gif] should be reduced by approximately [Graphics:Images/SimpsonRuleMod_gr_178.gif].  Explore this phenomenon.

Solution 10.

[Graphics:../Images/SimpsonRuleMod_gr_179.gif]
[Graphics:../Images/SimpsonRuleMod_gr_180.gif]

[Graphics:../Images/SimpsonRuleMod_gr_181.gif]
[Graphics:../Images/SimpsonRuleMod_gr_182.gif]

[Graphics:../Images/SimpsonRuleMod_gr_183.gif]
[Graphics:../Images/SimpsonRuleMod_gr_184.gif]

[Graphics:../Images/SimpsonRuleMod_gr_185.gif]
[Graphics:../Images/SimpsonRuleMod_gr_186.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004