Example 5.  Compare the error bounds for the three point and five point formulas.
5 (a).  Which is smaller [Graphics:Images/RichardsonExtrapMod_gr_139.gif]?  Can you justify it?  
5 (b).  Which is smaller [Graphics:Images/RichardsonExtrapMod_gr_140.gif]?   Can you justify it?  

Solution 5.

[Graphics:../Images/RichardsonExtrapMod_gr_141.gif]



[Graphics:../Images/RichardsonExtrapMod_gr_142.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_143.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_144.gif]



[Graphics:../Images/RichardsonExtrapMod_gr_145.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_146.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_147.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004