Differential Equations Solutions 109

Differential - Chapter 20 Solutions Solution of Ordinary Differential Equations CHALLENGE 20.1(Partial Solution See the programs on the website

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Unformatted text preview: Chapter 20 Solutions: Solution of Ordinary Differential Equations CHALLENGE 20.1. (Partial Solution) See the programs on the website. CHALLENGE 20.2. We need the real parts of all eigenvalues to be negative. This means 4 − t2 < 0 and −t < 0, so the equation is stable when t > 2. CHALLENGE 20.3. The polynomial is p(t) = yn + (t − tn )fn , so we compute p(tn+1 ) = yn + (tn+1 − tn )fn . CHALLENGE 20.4. The true solution is y (t) = t. We compute: tn 0 0.1 0.2 ... 1.0 Euler approximation 0 0 + 1 ∗ .1 = 0.1 .1 + 1 ∗ .1 = 0.2 ... .9 + 1 ∗ .1 = 1.0 Euler’s method is exact for this problem. 119 ...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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