Example 10.  When the step size is reduced by a factor of [Graphics:Images/MidpointRuleMod_gr_165.gif] the error term  [Graphics:Images/MidpointRuleMod_gr_166.gif] should be reduced by approximately  [Graphics:Images/MidpointRuleMod_gr_167.gif].  Explore this phenomenon.

Solution 10.

[Graphics:../Images/MidpointRuleMod_gr_168.gif]
[Graphics:../Images/MidpointRuleMod_gr_169.gif]


[Graphics:../Images/MidpointRuleMod_gr_170.gif]
[Graphics:../Images/MidpointRuleMod_gr_171.gif]


[Graphics:../Images/MidpointRuleMod_gr_172.gif]
[Graphics:../Images/MidpointRuleMod_gr_173.gif]


[Graphics:../Images/MidpointRuleMod_gr_174.gif]
[Graphics:../Images/MidpointRuleMod_gr_175.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004