1. Central Divided Difference
Major: All Engineering Majors
Authors: Autar Kaw, Sri Harsha Garapati
Numerical Methods for STEM undergraduates
11/16/2018

2. Definition . y
Slope at
f(x) x

3. Central Divided Difference

4. Example Example: Solution: The velocity of a rocket is given by where
given in m/s and
is given in seconds. Use central difference approximation of
the first derivative of
Use a step size of
to calculate the acceleration at
Solution:

5. Example (contd.)

6. Example (contd.) Hence The exact value of
can be calculated by differentiating as

7. Example (contd.) The absolute relative true error is

8. Effect Of Step Size Value of
Using Central Divided Difference difference method.

9. Effect of Step Size in Central Divided Difference Method
Initial step size=0.05

10. Effect of Step Size on Approximate Error
Initial step size=0.05

11. Effect of Step Size on Absolute Relative Approximate Error
Initial step size=0.05

12. Effect of Step Size on Least Number of Significant Digits Correct
Initial step size=0.05

13. Effect of Step Size on True Error
Initial step size=0.05

14. Effect of Step Size on Absolute Relative True Error
Initial step size=0.05