Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 9.4, Problem 2SA
To determine
To solve: For Monte Carlo simulation with using SDE initial value problem with giving condition in the problem by using matlab program.
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Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist?
Below are data on the population of a species of moths that inhabit an island and breed annually (then
die). Suppose the population model has the form
Pn= (1 + r) Pn-1 + f₂
where n is measured in years after 1995. That is, P = population in 1995, P₁ =population in 1996, etc.
(a) You are to determine the updating function for this population using the data in the table above. Which
of the following equations are valid for this model and can be used to find the parameters?
Select all correct choices.
r =
Year
1995
1996
1997
fl
moths
5000
6600
8520
E
66008520 r+μ
6600 5000.r+μ
=
(1 + r)5000+ μl
(1+r)6600+ fl
(1 + r)6600 + μl
6600 (1+r)8520 + μ
(b) Now use the equations to solve for the two paramaters.
✓ 6600 =
5000 =
8520 =
=
A "surge function" is used in a wide range of mathematical models of real-
world phenomenon, such as the level of medication in the bloodstream after an initial
dose of a drug. A general surge function is given by
-kt
S(t) = Ate
where A, k are both positive constants. Find the point of inflection of S(t).
Chapter 9 Solutions
Numerical Analysis
Ch. 9.1 - Find the period of the linear congruential...Ch. 9.1 - Find the period of the LCG defined by a=4,b=0,m=9...Ch. 9.1 - Approximate the area under the curve y=x2 for 0x1,...Ch. 9.1 - Approximate the area under the curve y=1x for 0x1,...Ch. 9.1 - Prob. 5ECh. 9.1 - Prove that u1=x21+x22 in the Box-Muller Rejection...Ch. 9.1 - Implement the Minimal Standard random number...Ch. 9.1 - Implement randu and find the Monte Carlo...Ch. 9.1 - (a) Using calculus, find the area bounded by the...Ch. 9.1 - Carry out the steps of Computer Problem 3 for the...
Ch. 9.1 - Use n=104 pseudo-random points to estimate the...Ch. 9.1 - Use n=104 pseudo-random points to estimate the...Ch. 9.1 - (a) Use calculus to evaluate the integral 01x2x,...Ch. 9.1 - Prob. 8CPCh. 9.1 - Prob. 9CPCh. 9.1 - Devise a Monte Carlo approximation problem that...Ch. 9.2 - Prob. 1CPCh. 9.2 - Prob. 2CPCh. 9.2 - Prob. 3CPCh. 9.2 - Prob. 4CPCh. 9.2 - Prob. 5CPCh. 9.2 - One of the best-known Monte Carlo problems is the...Ch. 9.2 - Prob. 7CPCh. 9.2 - Prob. 8CPCh. 9.2 - Prob. 9CPCh. 9.3 - Design a Monte Carlo simulation to estimate the...Ch. 9.3 - Calculate the mean escape time for the random...Ch. 9.3 - In a biased random walk, the probability of going...Ch. 9.3 - Prob. 4CPCh. 9.3 - Design a Monte Carlo simulation to estimate the...Ch. 9.3 - Calculate the mean escape time for Brownian motion...Ch. 9.3 - Prob. 7CPCh. 9.4 - Use Itos formula to show that the solutions of the...Ch. 9.4 - Use Itos formula to show that the solutions of the...Ch. 9.4 - Use Itos formula to show that the solutions of the...Ch. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Use the Euler-Maruyama Method to find approximate...Ch. 9.4 - Use the Euler-Maruyama Method to find approximate...Ch. 9.4 - Apply the Euler-Maruyama Method with step size...Ch. 9.4 - Prob. 4CPCh. 9.4 - Prob. 5CPCh. 9.4 - Prob. 6CPCh. 9.4 - Use the Milstein Method to find approximate...Ch. 9.4 - Prob. 8CPCh. 9.4 - Prob. 9CPCh. 9.4 - Prob. 10CPCh. 9.4 - Prob. 11CPCh. 9.4 - Prob. 12CPCh. 9.4 - Prob. 1SACh. 9.4 - Prob. 2SACh. 9.4 - Prob. 3SACh. 9.4 - Prob. 4SACh. 9.4 - Compare your approximation in step 4 with the...Ch. 9.4 - Prob. 6SA
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