hw3_solution

hw3_solution - Numerical Analysis in Engineering ME 140A,...

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Unformatted text preview: Numerical Analysis in Engineering ME 140A, Fall 2007 Homework #3 Solution By: Mohamad Nasr-Azadani [email protected] October 19, 2007 Problem 1 (19.1) One can use Figures 19.3, 19.4 and 19.5 to find Forward difference, Backward difference and Central difference derivatives, respectively. Forward Differencing formulas are given by f ( x i ) = f ( x i +1 )- f ( x i ) h ; O ( h ) (1) f ( x i ) =- f ( x i +2 ) + 4 f ( x i +1 )- 3 f ( x i ) 2 h ; O ( h 2 ) (2) For the given function, i.e. f ( x ) = cos ( x ) and parameters x i = π 4 , h = π 12 , one can find the derivatives using equations (1) and (2) as f ( x i ) =- . 79109 → t = 11 . 88% O ( h ) (3) f ( x i ) =- . 72601 → t = 2 . 67% O ( h 2 ) (4) Note that in equations (3) and (4), t (relative error) is defined as t =- sin ( x i )- f ( x i )- sin ( x i ) × 100 (5) For Backward Differencing , we have f ( x i ) = f ( x i )- f ( x i- 1 ) h ; O ( h ) (6) f ( x i ) = 3 f ( x i )- 4 f ( x i- 1 ) + f ( x i- 2 ) 2 h ; O ( h 2 ) (7) Therefore, for the given parameters, we have...
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This note was uploaded on 11/05/2009 for the course ME 140A taught by Professor Meiburg during the Fall '08 term at UCSB.

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hw3_solution - Numerical Analysis in Engineering ME 140A,...

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