Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 7.1, Problem 4CP
Carry out the steps of Computer Problem 3 for the nonlinear BVPs.
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(3) The approximate enrollment, in millions between the years 2009 and 2018 is
provided by a linear model
Y3D0.2309x+18.35
Where x-0 corresponds to 2009, x=1 to 2010, and so on, and y is in millions of
students.
Use the model determine projected enrollment for the
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2014.
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Problem 2. Consider the equation: x?y"(x) – xy' +y = 0. Given that yı(x) = x is a solution of this
equation. Use the method of reduction of order, find the second solution y2(x) of the equation so
that y1 and y2 are linearly independent. (Hint: y2(x) should be given in the form y2(x) = u(x)y1(x).
Substitute it into the equation to find u(x).)
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The same disease is spreading through two populations, say Pi and P2, with the same size. You may assume that the
spread of the disease is well described by the SIR model.
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YaIa
dt
with Sa(0) + I.(0) + R.(0) = N where N denotes the fixed population size. The subscript a identifies the
population P or P2. For example, if a = 1, the variables are related to P1. Assume that S1 (0) =
S2 (0) and I1(0) = I½(0) and that no interventions such as quarantine or vaccination have been implemented.
If the difference in the spread of the disease is due only to the poor over-all health of a population, which population
has the best over-all health of the two populations?
- Susceptible Population 1
- Susceptible Population 2
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Chapter 7 Solutions
Numerical Analysis
Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Apply the Shooting Method to the linear BVPs....
Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CPCh. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SACh. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SACh. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CPCh. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...
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