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1 Newton’s Divided Difference Polynomial Method of Interpolation

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http://numericalmethods.eng.usf.edu2 Newton’s Divided Difference Method Linear interpolation: Given pass a linear interpolant through the data where

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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 00 10227.04 15362.78 20517.35 22.5602.97 30901.67 Table 1: Velocity as a function of time Figure 2: Velocity vs. time data for the rocket example

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http://numericalmethods.eng.usf.edu4 Linear Interpolation

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http://numericalmethods.eng.usf.edu5 Linear Interpolation (contd)

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http://numericalmethods.eng.usf.edu6 Quadratic Interpolation

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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 00 10227.04 15362.78 20517.35 22.5602.97 30901.67 Table 1: Velocity as a function of time Figure 2: Velocity vs. time data for the rocket example

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8 Quadratic Interpolation (contd)

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http://numericalmethods.eng.usf.edu9 Quadratic Interpolation (contd)

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10 Quadratic Interpolation (contd)

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http://numericalmethods.eng.usf.edu11 General Form where Rewriting

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12 General Form

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http://numericalmethods.eng.usf.edu13 General form

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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 00 10227.04 15362.78 20517.35 22.5602.97 30901.67 Table 1: Velocity as a function of time Figure 2: Velocity vs. time data for the rocket example

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http://numericalmethods.eng.usf.edu15 Example The velocity profile is chosen as we need to choose four data points that are closest to

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16 Example

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http://numericalmethods.eng.usf.edu17 Example

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http://numericalmethods.eng.usf.edu18 Comparison Table

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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

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

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

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