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# HW2 - h = 0 1 and h = 0 05 by using the analytical solution...

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EMAE 250.100: Homework 2 January 20, 2011 1. For the following function: f ( x ) = 6 x 2 + sin x (a) [1pts] Using the ﬁrst forward ﬁnite divided diﬀerence method, compute the approximation of the ﬁrst derivative of the above function at x i = 1 where the step size h = x i +1 - x i = 0 . 1. Repeat the process for h = 0 . 05. (b) [1pt] Find the true value of f 0 (1) analytically. (c) [1pts] Compute the true fractional relative errors for both cases (when h = 0 . 1 and h = 0 . 05) by using the analytical solution from (b). (d) [1pts] Using the second forward ﬁnite divided diﬀerence method, compute the approximation of the second derivative of the above function at x i = 1 where the step size h = x i +1 - x i = 0 . 1. Repeat the process for h = 0 . 05 (e) [1pts] Find the true value of f 00 (1) analytically. (f) [1pts] Compute the true fractional relative errors for both cases (when
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Unformatted text preview: h = 0 . 1 and h = 0 . 05) by using the analytical solution from (e). 2. Determine the approximated root of the following function: f ( x ) =-5 x 3-4 x 2 + 3 x + 4 (a) [2pts] Using three iterations of the bisection method with the initial guesses of x l = 0 and x u = 1. First check if the initial guesses are properly selected. If not, choose another set of points. Also, determine the minimum number of iterations required for the desired error, E d = 0 . 01, where the absolute error is deﬁned by the size of the interval at each iteration step. (b) [2pts] Using three iterations of the false-position method with the same initial guesses. *Calculate down to four decimal places for all numerical computations. 1...
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