Example 5.  When the step size is reduced by a factor of [Graphics:Images/Simpson38RuleMod_gr_113.gif] the error term  [Graphics:Images/Simpson38RuleMod_gr_114.gif] should be reduced by approximately [Graphics:Images/Simpson38RuleMod_gr_115.gif].  Explore this phenomenon.

Solution 5.

[Graphics:../Images/Simpson38RuleMod_gr_116.gif]
[Graphics:../Images/Simpson38RuleMod_gr_117.gif]


[Graphics:../Images/Simpson38RuleMod_gr_118.gif]
[Graphics:../Images/Simpson38RuleMod_gr_119.gif]


[Graphics:../Images/Simpson38RuleMod_gr_120.gif]
[Graphics:../Images/Simpson38RuleMod_gr_121.gif]


[Graphics:../Images/Simpson38RuleMod_gr_122.gif]
[Graphics:../Images/Simpson38RuleMod_gr_123.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004