Question

To approximate the value of f'''(xk), the following formulas are used
f'''k =1/h^3[ fk+3 −3 fk+2 +3 fk+1 − fk]
f'''k =1/2h3[ fk+2 −2 fk+1 +2 fk−1 − fk−2]
Which formula do you find more accurate, and why?

Answer 1

f'''k =1/h^3[ fk+3 −3 fk+2 +3 fk+1 − fk]

Because,

The formula is central difference method which is equivalent to the average of forward and backward difference method