Example 17.  Given  [Graphics:Images/NumericalDiffMod_gr_388.gif], find numerical approximations to the second derivative  [Graphics:Images/NumericalDiffMod_gr_389.gif], using three points and the central difference formula.

Solution 17.

[Graphics:../Images/NumericalDiffMod_gr_390.gif]

[Graphics:../Images/NumericalDiffMod_gr_391.gif]

[Graphics:../Images/NumericalDiffMod_gr_392.gif]
[Graphics:../Images/NumericalDiffMod_gr_393.gif]

[Graphics:../Images/NumericalDiffMod_gr_394.gif]

[Graphics:../Images/NumericalDiffMod_gr_395.gif]
[Graphics:../Images/NumericalDiffMod_gr_396.gif]

[Graphics:../Images/NumericalDiffMod_gr_397.gif]

[Graphics:../Images/NumericalDiffMod_gr_398.gif]
[Graphics:../Images/NumericalDiffMod_gr_399.gif]

[Graphics:../Images/NumericalDiffMod_gr_400.gif]

[Graphics:../Images/NumericalDiffMod_gr_401.gif]
[Graphics:../Images/NumericalDiffMod_gr_402.gif]

[Graphics:../Images/NumericalDiffMod_gr_403.gif]

[Graphics:../Images/NumericalDiffMod_gr_404.gif]
[Graphics:../Images/NumericalDiffMod_gr_405.gif]

[Graphics:../Images/NumericalDiffMod_gr_406.gif]

[Graphics:../Images/NumericalDiffMod_gr_407.gif]
[Graphics:../Images/NumericalDiffMod_gr_408.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004