Example 2.  Graph  [Graphics:Images/RichardsonExtrapMod_gr_45.gif].  Find the bound  [Graphics:Images/RichardsonExtrapMod_gr_46.gif].   Look at a graph and estimate the value  [Graphics:Images/RichardsonExtrapMod_gr_47.gif], be sure to take the absolute value if necessary.

Solution 2.

[Graphics:../Images/RichardsonExtrapMod_gr_48.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_49.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_50.gif]

The minimum occurs at x = 0 and the maximum occurs at [Graphics:../Images/RichardsonExtrapMod_gr_51.gif] . Now find the formula for the error bound.

[Graphics:../Images/RichardsonExtrapMod_gr_52.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_53.gif] [Graphics:../Images/RichardsonExtrapMod_gr_54.gif] [Graphics:../Images/RichardsonExtrapMod_gr_55.gif] [Graphics:../Images/RichardsonExtrapMod_gr_56.gif] [Graphics:../Images/RichardsonExtrapMod_gr_57.gif]

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003