Presentation is loading. Please wait.

Presentation is loading. Please wait.

1 Newton’s Divided Difference Polynomial Method of Interpolation.

Similar presentations


Presentation on theme: "1 Newton’s Divided Difference Polynomial Method of Interpolation."— Presentation transcript:

1 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 3 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. tv(t) sm/s Table 1: Velocity as a function of time Figure 2: Velocity vs. time data for the rocket example

4 Linear Interpolation

5 Linear Interpolation (contd)

6 Quadratic Interpolation

7 7 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. tv(t) sm/s Table 1: Velocity as a function of time Figure 2: Velocity vs. time data for the rocket example

8 8 Quadratic Interpolation (contd)

9 Quadratic Interpolation (contd)

10 10 Quadratic Interpolation (contd)

11 General Form where Rewriting

12 12 General Form

13 General form

14 14 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. tv(t) sm/s Table 1: Velocity as a function of time Figure 2: Velocity vs. time data for the rocket example

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

16 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. xf(x) 0,00,000 0,20,406 0,40,846 0,61,368 0,82,060 1,03,114 1,25,114

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

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


Download ppt "1 Newton’s Divided Difference Polynomial Method of Interpolation."

Similar presentations


Ads by Google