HW10Solution - Homework 10 Solution 1 Given dy dx = 15(sin...

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Unformatted text preview: Homework 10 Solution 1. Given dy dx =- 15(sin x + y )- cos x (a) [1pt] If y(0) = 1, use the explicit Eulers method to obtain a solution from x = 0 to x = 1 with the step size, h = 0 . 5 . (b) [1pt] For the same initial values, use the implicit Eulers method to obtain a solution from x = 0 to x = 1 with h = 0 . 5. Q1: (a) explicit Eulers method f ( x,y ) =- 15(sin x + y )- cos x y 1 = y + f ( x ,y ) h = 1 + (- 16) . 5 =- 7 y 2 = y 1 + f ( x 1 ,y 1 ) h =- 7 + (96 . 9310) . 5 = 41 . 4655 (b) implicit Eulers method y 1 = y + f ( x 1 ,y 1 ) h = 1 + 0 . 5(- 15(sin 0 . 5 + y 1 )- cos 0 . 5) y 1 = 1- 7 . 5 sin 0 . 5- . 5 cos 0 . 5 8 . 5 =- . 3570 y 2 =- . 3570- 7 . 5 sin 1- . 5 cos 1 8 . 5 =- . 8163 2. [3pt] Consider the inverted pendulum shown in Lecture-Week 11, p12. If the massless rod is fixed with a rotational joint and the mass, m , is concentrated on the other end. For a small value of , this system can be solved using d 2 dt 2- g l = 0 For = (0) = 0, d (0) dt = 0 . 25[rad/s] and h = 0 . 1, first apply Heuns method to solve the...
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This note was uploaded on 11/14/2011 for the course EAME 250 taught by Professor Lee during the Spring '11 term at Case Western.

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HW10Solution - Homework 10 Solution 1 Given dy dx = 15(sin...

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