Example 8.  Given  [Graphics:Images/RichardsonExtrapMod_gr_172.gif], find numerical approximations to the derivative  [Graphics:Images/RichardsonExtrapMod_gr_173.gif], using five points and the central difference formula.

Solution 8.

[Graphics:../Images/RichardsonExtrapMod_gr_174.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_175.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_176.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_177.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_178.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_179.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_180.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_181.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_182.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_183.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_184.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_185.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_186.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_187.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_188.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_189.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_190.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_191.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_192.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004