Example 5.  When the step size is reduced by a factor of [Graphics:Images/MidpointRuleMod_gr_101.gif] the error term  [Graphics:Images/MidpointRuleMod_gr_102.gif] should be reduced by approximately  [Graphics:Images/MidpointRuleMod_gr_103.gif].  Explore this phenomenon.

Solution 5.

[Graphics:../Images/MidpointRuleMod_gr_104.gif]
[Graphics:../Images/MidpointRuleMod_gr_105.gif]


[Graphics:../Images/MidpointRuleMod_gr_106.gif]
[Graphics:../Images/MidpointRuleMod_gr_107.gif]


[Graphics:../Images/MidpointRuleMod_gr_108.gif]
[Graphics:../Images/MidpointRuleMod_gr_109.gif]


[Graphics:../Images/MidpointRuleMod_gr_110.gif]
[Graphics:../Images/MidpointRuleMod_gr_111.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004