Newtons Divided Difference Polynomial Method of Interpolation Major

Newton’s Divided Difference Polynomial Method of Interpolation Major: All Engineering Majors Authors: Autar Kaw, Jai Paul http: //numericalmethods. eng. usf. edu Transforming Numerical Methods Education for STEM Undergraduates http: //numericalmethods. eng. usf. edu 1

Newton’s Divided Difference Method of Interpolation http: //numericalmethods. eng. usf. edu

What is Interpolation ? Given (x 0, y 0), (x 1, y 1), …… (xn, yn), find the value of ‘y’ at a value of ‘x’ that is not given. 3 lmethods. eng. usf. edu http: //numerica

Interpolants Polynomials are the most common choice of interpolants because they are easy to: Evaluate Differentiate, and Integrate. 4 lmethods. eng. usf. edu http: //numerica

Newton’s Divided Difference Method Linear interpolation: Given linear interpolant through the data pass a where 5 lmethods. eng. usf. edu http: //numerica

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. Table. Velocity as a function of time 0 10 15 20 22. 5 30 6 0 227. 04 362. 78 517. 35 602. 97 901. 67 Figure. Velocity vs. time data for the rocket examplelmethods. eng. usf. edu http: //numerica

Linear Interpolation 7 lmethods. eng. usf. edu http: //numerica

Linear Interpolation (contd) 8 lmethods. eng. usf. edu http: //numerica

Quadratic Interpolation 9 lmethods. eng. usf. edu http: //numerica

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. Table. Velocity as a function of time 0 10 15 20 22. 5 30 10 0 227. 04 362. 78 517. 35 602. 97 901. 67 Figure. Velocity vs. time data for the rocket examplelmethods. eng. usf. edu http: //numerica

Quadratic Interpolation (contd) 11 lmethods. eng. usf. edu http: //numerica

Quadratic Interpolation (contd) 12 lmethods. eng. usf. edu http: //numerica

Quadratic Interpolation (contd) 13 lmethods. eng. usf. edu http: //numerica

General Form where Rewriting 14 lmethods. eng. usf. edu http: //numerica

General Form 15 lmethods. eng. usf. edu http: //numerica

General form 16 lmethods. eng. usf. edu http: //numerica

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. Table. Velocity as a function of time 0 10 15 20 22. 5 30 17 0 227. 04 362. 78 517. 35 602. 97 901. 67 Figure. Velocity vs. time data for the rocket examplelmethods. eng. usf. edu http: //numerica

Example The velocity profile is chosen as we need to choose four data points that are closest to 18 lmethods. eng. usf. edu http: //numerica

Example 19 lmethods. eng. usf. edu http: //numerica

Example 20 lmethods. eng. usf. edu http: //numerica

Comparison Table 21 lmethods. eng. usf. edu http: //numerica

Distance from Velocity Profile Find the distance covered by the rocket from t=11 s to t=16 s ? 22 lmethods. eng. usf. edu http: //numerica

Acceleration from Velocity Profile Find the acceleration of the rocket at t=16 s given that 23 lmethods. eng. usf. edu http: //numerica

Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, Math. Cad and MAPLE, blogs, related physical problems, please visit http: //numericalmethods. eng. usf. edu/topics/newton_div ided_difference_method. html

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