mws_gen_dif_spe_backward - Backward Divided Difference...

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5/21/2008 http://numericalmethods.eng.usf.edu 1 Backward 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 i x . () ( ) ( ) x x x f x f x x f Δ Δ Δ = 0 lim Slope at f(x) y x
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http://numericalmethods.eng.usf.edu 3 Backward Divided Difference x x Δ x x () ( ) x x x f x f x f Δ Δ ( ) x x x f x f x f i i i Δ Δ ) ( x f
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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 backward 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 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 14 2 16 = = () 2 14 16 16 ν = a 16 8 . 9 16 2100 10 14 10 14 ln 2000 16 4 4 ×
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mws_gen_dif_spe_backward - Backward Divided Difference...

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