Differential Equations Solutions 119

Differential Equations Solutions 119 - respect to x so that...

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Chapter 21 Solutions: Case Study: More Models of Infection: It’s Epidemic CHALLENGE 21.1. Sample programs are given on the website. The results are shown in Figure 21.1. 95.3% of the population becomes infected. CHALLENGE 21.2. The results are shown in Figure 21.1 and, as expected, are indistinguishable from those of Model 1. CHALLENGE 21.3. The results are shown in Figure 21.2. 94.3% of the population becomes infected, slightly less than in the ±rst models, and the epidemic dies out in roughly half the time. CHALLENGE 21.4. Let’s use subscripts x to denote partial derivatives with
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Unformatted text preview: respect to x , so that I xx ( t, x, y ) = ∂ 2 I ( t, x, y ) /∂x 2 . (a) Since Taylor series expansion yields I ( t ) i − 1 ,j = I ( t, x, y ) − hI x ( t, x, y ) + h 2 2 I xx ( t, x, y ) − h 3 6 I xxx ( t, x, y ) + O ( h 4 ) , I ( t ) i +1 ,j = I ( t, x, y ) + hI x ( t, x, y ) + h 2 2 I xx ( t, x, y ) + h 3 6 I xxx ( t, x, y ) + O ( h 4 ) , we see that I ( t ) i − 1 ,j − 2 I ( t ) ij + I ( t ) i +1 ,j h 2 = h 2 I xx ( t, x, y ) + O ( h 4 ) h 2 = I xx ( t, x, y ) + O ( h 2 ) . 129...
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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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