5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: dN = 0.25N(10 – N), N(0) = 2 dt (a) where N is measured in 100's. Analyze the behavior of this differential equation as follows. d. Compute the time t when N is changing the fastest using the initial condition N(0) = 2. Compare your answer to your qualitative estimate in part a(iii) above. e. Use Euler's Method with step sizes of h = 1 and then h = 0.1 to approximate the solution to the differential equation for N(0.5) and N(5). Find the relative error at %3D
5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: dN = 0.25N(10 – N), N(0) = 2 dt (a) where N is measured in 100's. Analyze the behavior of this differential equation as follows. d. Compute the time t when N is changing the fastest using the initial condition N(0) = 2. Compare your answer to your qualitative estimate in part a(iii) above. e. Use Euler's Method with step sizes of h = 1 and then h = 0.1 to approximate the solution to the differential equation for N(0.5) and N(5). Find the relative error at %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. The Spread of a Contagious Disease. Consider the following ordinary differential
equation model for the spread of a communicable disease:
dN
= 0.25N(10 – N), N(0) = 2
dt
(a)
|
where N is measured in 100's. Analyze the behavior of this differential equation as
follows.
hloi
d. Compute the time t when N is changing the fastest using the initial condition N(0) =
2. Compare your answer to your qualitative estimate in part a(iii) above.
%3D
= 0.1 to approximate the
solution to the differential equation for N(0.5) and N(5). Find the relative error at
moo mo these values. Obtain graphical plots of the numerical solution. How do they compare
se. Use Euler's Method with step sizes of h = 1 and then h
%3D
er to the plots of the actual solution?
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