# HW2 - Homework 2 due Wednesday January 21 9am in class Note...

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Homework 2, due Wednesday January 21, 9am in class Note: Please turn in the programming problem separately from the theory problems. 1. (0.5 point each part) For each of the following constant-coeﬃcient sys- tems y 0 = Ay , determine if the system is stable, asymptotically stable, or unstable: (a) A = ± - 1 0 0 - 20 ² (b) A = ± 1 3 3 1 ² (c) A = ± - 1 10 0 2 ² (d) A = ± 0 - 1 1 0 ² 2. (5 points) Consider the method of lines applied to the diﬀusion equation in one space dimension, u t = au xx , with a > 0 a constant, u = 0 at x = 0, x = 1 for t 0, and with given initial values. Formulate the method of lines using the central diﬀerence approximation to the derivative, as in Example 1.3 of the text (as we did in Lecture 1), to arrive at a linear constant coeﬃcient ODE system y 0 = Ay

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HW2 - Homework 2 due Wednesday January 21 9am in class Note...

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