Differential Equations Solutions 119

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

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online