Example 10.  Given  [Graphics:Images/RichardsonExtrapMod_gr_214.gif], find numerical approximations to the derivative  [Graphics:Images/RichardsonExtrapMod_gr_215.gif], using five points and the central difference formula.

Solution 10.

[Graphics:../Images/RichardsonExtrapMod_gr_216.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_217.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_218.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_219.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_220.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_221.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_222.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_223.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_224.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_225.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_226.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_227.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_228.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_229.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_230.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_231.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_232.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_233.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_234.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004