Example 16.   Given  [Graphics:Images/NumericalDiffMod_gr_367.gif], find numerical approximations to the second derivative  [Graphics:Images/NumericalDiffMod_gr_368.gif], using three points and the backward difference formula.

Solution 16.

[Graphics:../Images/NumericalDiffMod_gr_369.gif]

[Graphics:../Images/NumericalDiffMod_gr_370.gif]

[Graphics:../Images/NumericalDiffMod_gr_371.gif]
[Graphics:../Images/NumericalDiffMod_gr_372.gif]

[Graphics:../Images/NumericalDiffMod_gr_373.gif]

[Graphics:../Images/NumericalDiffMod_gr_374.gif]
[Graphics:../Images/NumericalDiffMod_gr_375.gif]

[Graphics:../Images/NumericalDiffMod_gr_376.gif]

[Graphics:../Images/NumericalDiffMod_gr_377.gif]
[Graphics:../Images/NumericalDiffMod_gr_378.gif]

[Graphics:../Images/NumericalDiffMod_gr_379.gif]

[Graphics:../Images/NumericalDiffMod_gr_380.gif]
[Graphics:../Images/NumericalDiffMod_gr_381.gif]

[Graphics:../Images/NumericalDiffMod_gr_382.gif]

[Graphics:../Images/NumericalDiffMod_gr_383.gif]
[Graphics:../Images/NumericalDiffMod_gr_384.gif]

[Graphics:../Images/NumericalDiffMod_gr_385.gif]

[Graphics:../Images/NumericalDiffMod_gr_386.gif]
[Graphics:../Images/NumericalDiffMod_gr_387.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004