mws_gen_dif_spe_central - Central Divided Difference Topic:...

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5/21/2008 http://numericalmethods.eng.usf.edu 1 Central Divided Difference Topic: Differentiation Major: General Engineering Authors: Autar Kaw, Sri Harsha Garapati
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http://numericalmethods.eng.usf.edu 2 Definition i x . () ( ) ( ) x x x f x f x x f Δ Δ Δ = 0 lim f(x) Slope at x y i x
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http://numericalmethods.eng.usf.edu 3 Central Divided Difference x x Δ + x x () ( ) ( ) x x x f x x f x f Δ Δ Δ + 2 ( )( ) x x x f x x f x f i i i Δ Δ Δ + 2 ) ( x f x x Δ
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http://numericalmethods.eng.usf.edu 4 Example Example : The velocity of a rocket is given by () 30 0 , 8 . 9 2100 10 14 10 14 ln 2000 4 4 × × = t t t t ν where given in m/s and t is given in seconds . Use central difference approximation of the first derivative of ( ) t ν to calculate the acceleration at . 16 s t = Use a step size of . 2 s t = Δ ( ) ( ) t t t t a i i i Δ + 2 1 1 Solution: 16 = i t
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http://numericalmethods.eng.usf.edu 5 2 Δ = t t t t i i Δ 1 + = + 18 2 16 = + = () ( ) ( ) 4 14 18 ) 2 ( 2 14 18 16 ν = = a 18 8 . 9 18 2100 10 14 10 14 ln 2000 18 4 4
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_gen_dif_spe_central - Central Divided Difference Topic:...

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