HW12suggestions

# HW12suggestions - (a Euler h = 0 1 and h = 0 2(b...

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Jacobs University, Bremen School of Engineering and Science Prof. Dr. Lars Linsen, Orif Ibrogimov Spring Term 2010 Homework 12 120202: ESM4A - Numerical Methods Homework Problems 12.1. (a) Solve the initial-value problem x 0 = 1 + x 2 and x (0) = 0 on the interval [0 , 1 . 56] using the Taylor-series method of order four with step h = 0 . 01. (b) Solve the initial-value problem x 0 = - 3 t 2 x + x 2 2 t 3 + 3 tx and x (1) = - 2 on the interval [0 , 1] using the Taylor-series method of order two with step h = - 0 . 01. ( ? points ) 12.2. The function y ( x ) is deﬁned by the problem y 0 ( x ) = x 2 - y 2 and y (0) = 1 Compute y (0 . 02) using the following methods
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Unformatted text preview: (a) Euler: h = 0 . 1 and h = 0 . 2; (b) Runge-Kutta method: h = 0 . 1; (c) Taylor-series method of order four. ( ? points ) 12.3. Given the initial value problem y ( t ) = ( y ( t ) + t ) 2 and y (0) = 1. Let step size h = 0 . 01. (a) Execute two steps of the second-order Runge-Kutta method. (b) Execute two steps of the fourth-order Runge-Kutta method. ( ? points ) Due: 14.05.10, at 3 pm (in the mailbox labeled Linsen in the entrance hall of Res.I )...
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