Example 10.  When the step size is reduced by a factor of [Graphics:Images/Simpson38RuleMod_gr_172.gif] the error term  [Graphics:Images/Simpson38RuleMod_gr_173.gif] should be reduced by approximately [Graphics:Images/Simpson38RuleMod_gr_174.gif].  Explore this phenomenon.

Solution 10.

[Graphics:../Images/Simpson38RuleMod_gr_175.gif]
[Graphics:../Images/Simpson38RuleMod_gr_176.gif]


[Graphics:../Images/Simpson38RuleMod_gr_177.gif]
[Graphics:../Images/Simpson38RuleMod_gr_178.gif]


[Graphics:../Images/Simpson38RuleMod_gr_179.gif]
[Graphics:../Images/Simpson38RuleMod_gr_180.gif]


[Graphics:../Images/Simpson38RuleMod_gr_181.gif]
[Graphics:../Images/Simpson38RuleMod_gr_182.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004