These formulas below approximate at where is the grid point number.
For example, to obtain the third formula above, we start from Taylor series and write
then we write it again for the previous point
Notice the sign change in the expressions. We now subtract the second formula above from the above resulting in
or
These formulas below approximate at where is the grid point number. For approximation to the accuracy of the approximation formula must be no less than .
To obtain the third formula above, we start from Taylor series and write
Then we write it again for the previous point
Notice the sign change in the expressions. We now add the second formula above from the above resulting in