mws_gen_inp_ppt_ndd

mws_gen_inp_ppt_ndd - Newtons Divided Difference Polynomial...

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http://numericalmethods.eng.usf.edu 1 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
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Newton’s Divided Difference Method of Interpolation http://numericalmethods.eng.usf.edu
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http://numericalmethods.eng.usf.edu 3 What is Interpolation ? Given (x 0 ,y 0 ), (x 1 ,y 1 ), …… (x n ,y n ), find the value of ‘y’ at a value of ‘x’ that is not given.
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http://numericalmethods.eng.usf.edu 4 Interpolants Polynomials are the most common choice of interpolants because they are easy to: Evaluate Differentiate, and Integrate .
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http://numericalmethods.eng.usf.edu 5 Newton’s Divided Difference Method Linear interpolation : Given pass a linear interpolant through the data where ), , ( 0 0 y x ), , ( 1 1 y x ) ( ) ( 0 1 0 1 x x b b x f + = ) ( 0 0 x f b = 0 1 0 1 1 ) ( ) ( x x x f x f b =
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http://numericalmethods.eng.usf.edu 6 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 Figure. Velocity vs. time data for the rocket example 0 0 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 ) s ( t ) m/s ( ) ( t v
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http://numericalmethods.eng.usf.edu 7 Linear Interpolation 10 12 14 16 18 20 22 24 350 400 450 500 550 517.35 362.78 y s f range ( ) f x desired ( ) x s 1 10 + x s 0 10 x s range , x desired , , 15 0 = t 78 . 362 ) ( 0 = t v , 20 1 = t 35 . 517 ) ( 1 = t v ) ( 0 0 t v b = 78 . 362 = 0 1 0 1 1 ) ( ) ( t t t v t v b = 914 . 30 = ) ( ) ( 0 1 0 t t b b t v + =
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8 Linear Interpolation (contd) 10 12 14 16 18 20 22 24 350 400 450 500 550 517.35 362.78 y s f range ( ) f x desired ( ) x s 1 10 + x s 0 10 x s range , x desired , ) ( ) ( 0 1 0 t t b b t v + = ), 15 ( 914 . 30
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mws_gen_inp_ppt_ndd - Newtons Divided Difference Polynomial...

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