In this exercise, difference approximations are derived that make use of derivative information. (a) Find a ( 2 ) approximation of ”( j +1 ) and uses  ’ ( j +1 ) and ’ ( j −1 ). (b) Find a ( 2 )...

In this exercise, difference approximations are derived that make use of derivative information.

(a) Find a
(
²) approximation of
”(

_j+1) and uses
 ’ (

_j+1) and
’ (

_j−1).

(b) Find a
(
²) approximation of
’ (

_j+1) and uses
(

_j

),
(

_j+1), and
 ’ (

_j

).

(c) Find a
(
⁴) approximation of
 ‘ (

_j+1) and uses
(

_j−1),
(

_j+1),
 ’ (

_j

), and
’ (

_j−1).