Example 15.   Given  [Graphics:Images/NumericalDiffMod_gr_346.gif], find numerical approximations to the second derivative  [Graphics:Images/NumericalDiffMod_gr_347.gif], using three points and the forward difference formula.

Solution 15.

[Graphics:../Images/NumericalDiffMod_gr_348.gif]

[Graphics:../Images/NumericalDiffMod_gr_349.gif]

[Graphics:../Images/NumericalDiffMod_gr_350.gif]
[Graphics:../Images/NumericalDiffMod_gr_351.gif]

[Graphics:../Images/NumericalDiffMod_gr_352.gif]

[Graphics:../Images/NumericalDiffMod_gr_353.gif]
[Graphics:../Images/NumericalDiffMod_gr_354.gif]

[Graphics:../Images/NumericalDiffMod_gr_355.gif]

[Graphics:../Images/NumericalDiffMod_gr_356.gif]
[Graphics:../Images/NumericalDiffMod_gr_357.gif]

[Graphics:../Images/NumericalDiffMod_gr_358.gif]

[Graphics:../Images/NumericalDiffMod_gr_359.gif]
[Graphics:../Images/NumericalDiffMod_gr_360.gif]

[Graphics:../Images/NumericalDiffMod_gr_361.gif]

[Graphics:../Images/NumericalDiffMod_gr_362.gif]
[Graphics:../Images/NumericalDiffMod_gr_363.gif]

[Graphics:../Images/NumericalDiffMod_gr_364.gif]

[Graphics:../Images/NumericalDiffMod_gr_365.gif]
[Graphics:../Images/NumericalDiffMod_gr_366.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004