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# HW9 - (c[1pt using the midpoint method(d[1pt using the...

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EMAE 250: Homework 9 April 1, 2011 1. Given the following function: f ( x ) = 3 x 4 - 4 x 3 + 2 x - 5 (a) [1.5pt] find the estimate of the first and second derivatives using the forward finite divided difference (FFDD) formulas by truncating after the first term at x = 0 . 5 and h = 0 . 25. (b) [1.5pt] repeat (a) using the FFDD formulas by keeping the first two terms. (c) [1pt] find an analytical solution and compute t for (a) and (b) 2. Numerically solve the following differential equation from x = 0 to x = 0 . 5 using h = 0 . 25: dy dx = 3 x - 2 y where y | x =0 = y (0) = 2. (a) [1pt] using the Euler’s method. (b) [1pt] using the Heun’s method.
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Unformatted text preview: (c) [1pt] using the midpoint method. (d) [1pt] using the 3rd-order Runge-Kutta method. (e) [1pt] using the 4th-order Runge-Kutta method. (f) [1pt] The analytical solution of the given diﬀerential equation is y = 2 . 75 e-2 x + 1 . 5 x-. 75. Using the above formula, compute y t (0 . 5) and then ﬁnd the fractional relative error for (a) - (e) and discuss the results. ± t = ± ± ± ± ± y t-y a y t ± ± ± ± ± × 100% where y t is the analytical solution and y a is an approximation using numerical meth-ods in (a)-(e). 1...
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