1. Newton’s Divided Difference Polynomial Method of Interpolation

2. Newton’s Divided Difference Method
Linear interpolation: Given pass a linear interpolant through the data
where

3. Figure 2: Velocity vs. time data
Example
The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for linear interpolation. t
v(t) s
m/s 10
227.04 15
362.78 20
517.35
22.5
602.97 30
901.67
Figure 2: Velocity vs. time data
for the rocket example
Table 1: Velocity as a
function of time

4. Linear Interpolation

5. Linear Interpolation (contd)

6. Quadratic Interpolation

7. Figure 2: Velocity vs. time data
Example
The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for quadratic interpolation. t
v(t) s
m/s 10
227.04 15
362.78 20
517.35
22.5
602.97 30
901.67
Figure 2: Velocity vs. time data
for the rocket example
Table 1: Velocity as a
function of time

8. Quadratic Interpolation (contd)

9. Quadratic Interpolation (contd)

10. Quadratic Interpolation (contd)

11. General Form
where
Rewriting

12. General Form

13. General form

14. Figure 2: Velocity vs. time data
Example
The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the Newton Divided Difference method for cubic interpolation. t
v(t) s
m/s 10
227.04 15
362.78 20
517.35
22.5
602.97 30
901.67
Figure 2: Velocity vs. time data
for the rocket example
Table 1: Velocity as a
function of time

15. Example The velocity profile is chosen as
we need to choose four data points that are closest to

16. Example

17. Example

18. Comparison Table

19. Latihan
Misalkan Nilai-nilai fungsi seperti pada tabel berikut, tentukanlah nilai aproksimasi dari f(0,1), f(0,35), dan f(1,16) berturut-turut menggunakan interpolasi beda terbagi Newton linear, kuadratik, kubik. x
f(x)
0,0
0,000
0,2
0,406
0,4
0,846
0,6
1,368
0,8
2,060
1,0
3,114
1,2
5,114

20. Distance from Velocity Profile
Find the distance covered by the rocket from t=11s to
t=16s ?

21. Acceleration from Velocity Profile
Find the acceleration of the rocket at t=16s given that